Direct links:

ORCID: 0000-0003-2528-8357

Education

Awards

Research lines

Publications

Ph. D. Students

Conferences

Research Projects

Talks in Seminars

Functional Analysis group in Granada >>web

  
 

 

 

  

Research:

Education:

  • B.Sc. in Mathematics, Universidad de Granada, Spain. 1992-1997.
  • M.A. Universidad de Granada, Spain. December 1997.
  • Ph.D. in Mathematics, Universidad de Granada, Spain. September 20th, 2000 ("sobresaliente cum laude", Awarded with "Premio extraordinario de doctorado, 1999-2000").

Awards:

Membership in Editorial Boards

Research lines:

  • Functional Analysis: C*-algebras, von Neumann algebras, JB*-algebras, JB*-triples and operator theory
  • Geometric properties (isomorphic and isometric) on C*-algebras, JB*-triples and their duals:
    • Dunford-Pettis property,
    • Alternative Dunford-Pettis property
    • Kadec-Klee property
    • Banach-Stone type theorems for real and complex JB*-triples
  • C*- and JB*-summing operators from C*-algebras and JB*-triples to Banach spaces
  • Grothendieck inequalities in real and complex JB*-triples
  • Structure theory for real and complex JB*-triples
  • Orthogonally Preservers between C*-algebras and JB*-triples
  • Extension of isometries, Tingley's problem, Mazur-Ulam property.
  • Linear and non-linear Presevers.
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Expository papers:

M.S. Moslehian and A. Peralta, Predatory Journals Pose a Threat to the Dissemination of Science, Notices of Amer. Math. Soc. 71 (2024), no. 9, 1177-1179.

List of Publicatios:

162 Lei Li, Siyu Liu, Antonio M. Peralta, Additive mappings preserving orthogonality between complex inner product spaces, preprint 2024.
arXiv: 2410.08101
161 Gerardo M. Escolano, Antonio M. Peralta, Armando R. Villena, Preservers of Operator Commutativity, Preprint 2024. arXiv: 2409.06799
160 Jorge J. Garcés, Lei Li, Antonio M. Peralta, Shan Shan Su, Maps preserving the truncation of triple products on Cartan factors, Preprint 2024. arXiv: 2405.13489
159 David P. Blecher, Matthew Neal, Antonio M. Peralta, Shanshan Su, M-Ideals in Real Operator Algebras. Preprint 2024. arXiv:2405.05383
158 Amin Hosseini, Antonio M. Peralta and Shanshan Su, On the equivalence of all notions of generalized derivations whose domain is a C*-algebra. Preprint 2024. arXiv: 2403.18773
157 David P. Blecher, Matthew Neal, Antonio M. Peralta, Shanshan Su, M-ideals, yet again: the case of real JB*-triples, Preprint 2024. arXiv: 2401.05565
156 Antonio M. Peralta, Metric invariants in Banach and Jordan--Banach algebras, Proceedings of Symposia in Pure Mathematics (PUPUM). Godefroy, Gilles (ed.) et al., Geometry of Banach spaces and related fields. Dedicated to Professor Per. Enflo.Providence, RI: American Mathematical Society (AMS). Proc. Symp. Pure Math. 106, 251-346 (2024).
arXiv:2308.16788
155 Gerardo M. Escolano, Antonio M. Peralta, Armando R. Villena, Lie-Trotter formulae in Jordan--Banach algebras with applications to the study of spectral-valued multiplicative functionals, to appear in Results in Math. 79, 17 (2024). https://doi.org/10.1007/s00025-023-02043-w
arXiv:2305.05530
154 David Cabezas, Antonio M. Peralta, Estimations of the numerical index of a JB*-triple, to appear in Bull. Malaysian Math. Sci. Soc.47, 8 (2024). https://doi.org/10.1007/s40840-023-01598-9. arXiv:2302.14773
153

Antonio M. Peralta, Radovan Svarc, A strengthened Kadison's transitivity theorem for unital JB*-algebras with applications to the Mazur--Ulam property, preprint 2023.
arXiv: 2301.00895

152

 David Cabezas, María Cueto-Avellaneda, Yuta Enami, Takeshi Miura, Antonio M. Peralta, Tingley's problem for complex Banach spaces which do not satisfy the Hausdorff distance condition, Banach J. Math. Anal. 17 (2023): 65.
https://doi.org/10.1007/s43037-023-00291-0
arXiv: 2210.17131

151

Francisco J. Fernández-Polo, Jorge J. Garcés, Lei Li, Antonio M. Peralta, On the strict topology of the multipliers of a JB*-algebra, RACSAM 117 (2023), no. 4, Paper No. 146, 27 pp.
https://doi.org/10.1007/s13398-023-01476-w. arXiv: 2210.13353

150

Antonio M. Peralta, Preservers of triple transition pseudo-probabilities in connection with orthogonality preservers and surjective isometries, Results Math. (2023) 78:51.
https://doi.org/10.1007/s00025-022-01827-w
arXiv:2208.01464

149

David Cabezas, Miguel Martín, Antonio M. Peralta, The Daugavet equation for polynomials on C*-algebras and JB*-triples, Advances in Mathematics 439, Article ID 109479, 22 p. (2024). DOI: 10.1016/j.aim.2023.109479. arXiv:2206.11621

148.

D. Cabezas, A.M. Peralta, Linear orthogonality preservers between function spaces associated with commutative JB*-triples, to appear in Linear Multilinear Algebra 71 (2023), 2728-2743.
https://doi.org/10.1080/03081087.2022.2119466
arXiv:2205.11176

147.

J.J. Garcés, L. Li, A.M. Peralta, H.M. Tahlawi, A projection–less approach to Rickart Jordan structures, J. Algebra 609 (2022), 567–605. arXiv: 2202.08140

146.

D. Cabezas, M. Cueto-Avellaneda, D. Hirota, T. Miura, A.M. Peralta, Every commutative JB*-triple satisfies the complex Mazur–Ulam property,  Ann. Funct. Anal. 13 (2022), no. 4, Paper No. 60, 8 pp. arXiv: 2201.06307

145.

J. Hamhalter, O.F.K. Kalenda, A.M. Peralta, Order type relations on the set of tripotents in a JB*-triple, preprint 2021. arXiv: 2112.03155

144.

A.M. Peralta, Maps preserving triple transition pseudo-probabilities, RIMS Kôkyûroku Bessatsu B93 (2023), 3?30 (ISSN: 1881-6193).
arXiv: 2204.03463

143.

M. Cueto-Avellaneda, D. Hirota, T. Miura, A.M. Peralta, Exploring new solutions to Tingley’s problem for function algebras, to appear in Quaestiones Mathematicae. https://doi.org/10.2989/16073606.2022.2072787 arXiv:2110.11120

142.

J. Hamhalter, O.F.K. Kalenda, A.M. Peralta, Determinants in Jordan matrix algebras, to appear in Linear and Multilinear Algebra. https://doi.org/10.1080/03081087.2022.2049187
arXiv:2110.10458

141.

A.M. Peralta, On the extension of surjective isometries whose domain is the unit sphere of a space of compact operators, 36:9 (2022), 3075-3090.
https://doi.org/10.2298/FIL2209075P

arXiv:2005.11987v1

140.

M. Cueto-Avellaneda, Y. Enami, D. Hirota, T. Miura, A.M. Peralta, Surjective isometries between unitary sets of unital JB$*-algebras, Linear Algebra Appl. 643 (2022), 39-79.
https://doi.org/10.1016/j.laa.2022.02.003.  arXiv:2105.14870

139.

M. Cueto, A.M. Peralta, Can one identify two unital JB*-algebras by the metric spaces determined by their sets of unitaries?, to appear in Linear and Multilinear Algebra
DOI: 10.1080/03081087.2021.2003745 arXiv:2005.04794

138.

O. Kalenda, A.M. Peralta, H. Pfitzner, On optimality of constants in the Little Grothendieck Theorem, Studia Math. 264 (3) (2022), 263-304. arXiv: 2002.12273

137.

M.S. Moslehian, G.A. Muñoz-Fernández, A.M. Peralta, J.B. Seoane-Sepúlveda, Similarities and differences between real and complex Banach spaces: an overview and recent developments, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 116 (2022), no. 2, Paper No. 88. arXiv:2107.03740

136.

Y. Friedman, A.M. Peralta, Representation of symmetry transformations on the sets of tripotents of spin and Cartan factors, Anal. Math. Phys. 12 (2022), no. 1, Paper No. 37, 52 pp. arXiv: 2101.00670

135.

A.M. Peralta, Surjective isometries between sets of invertible elements in unital Jordan-Banach algebras, J. Math. Anal. Appl. 502 (2021), 125284. DOI:https://doi.org/10.1016/j.jmaa.2021.125284

134.

J.J. Garcés, A.M. Peralta, One-parameter groups of orthogonality preservers on JB*-algebras, Advances in Operator Theory 6 (2021), 43. arXiv:2010.08129

133.

A. Ben Ali Essaleh, A.M. Peralta, A linear preserver problem on maps which are triple derivable at orthogonal pairs, RACSAM 115 (2021): 146. arXiv:2009.10336

132.

J.J. Garcés, A.M. Peralta, One-parameter groups of orthogonality preservers on C*-algebras, to appear in Banach J. Math. Anal. 15 (2021), no. 1, Paper No. 24, 23 pp. DOI: 10.1007/s43037-020-00100-y. arXiv:2004.04155v1

131.

O.F.K. Kalenda, A.M. Peralta, Extension of isometries from the unit sphere of a rank-2 Cartan factor, Anal. Math. Phys. 11, 15 (2021). arXiv:1907.00575

130.

J. Hamhalter, O. Kalenda, A.M. Peralta, H. Pfitzner, Grothendieck's inequalities for JB*-triples: Proof of the Barton-Friedman conjecture, Transactions of the American Mathematical Society 374, Number 2 (2021), 1327-1350. arXiv:1903.08931

129.

 J. Becerra Guerrero, M. Cueto, F.J. Fernández-Polo, A.M. Peralta, On the extension of isometries between the unit spheres of a JBW*-triple and a Banach space, J. Inst. Math. Jussieu 20 (2021), no. 1, 277-303. doi:10.1017/S1474748019000173

128.

J. Hamhalter, O. Kalenda, A.M. Peralta, Finite tripotents and finite JBW*-triples, J. Math. Anal. Appl. 490 (2020), 124217. https://doi.org/10.1016/j.jmaa.2020.124217 arXiv: 1911.08254v1

127.

D.A. Abulhamail, F.B. Jamjoom, A.M. Peralta, Linear maps which are anti-derivable at zero, Bull. Malays. Math. Sci. Soc. 43: 4315-4334 (2020). https://doi.org/10.1007/s40840-020-00918-7 arXiv: 1911.04134v1

126.

M. Cueto, A.M. Peralta, Metric characterisation of unitaries in JB*-algebras, Mediterr. J. Math. (2020) 17:124. DOI: 10.1007/s00009-020-01556-w arXiv:1907.04738

125.

J. Hamhalter, O. Kalenda, A.M. Peralta, H. Pfitzner, Measures of weak non-compactness in preduals of von Neumann algebras and JBW*-triples, Journal of Functional Analysis, 278 (2020), no. 1, 108300. https://doi.org/10.1016/j.jfa.2019.108300 arXiv:1901.08056v1

124.

M. Cueto, A.M. Peralta, The Mazur-Ulam property for commutative von Neumann algebras, Linear and Multilinear Algebra 68, No. 2, 337-362 (2020). https://doi.org/10.1080/03081087.2018.1505823.

123.

F.J. Fernández-Polo, E. Jordá, A.M. Peralta, Tingley's problem for $p$-Schatten von Neumann classes, J. Spectr. Theory 10 (3), 809-841 (2020). DOI 10.4171/JST/313 arXiv:1803.00763v1.

122.

M. Cueto, A.M. Peralta, On the Mazur--Ulam property for the space of Hilbert-space-valued continuous functions, J. Math. Anal. Appl. 479 (2019), 875-902. DOI: 10.1016/j.jmaa.2019.06.056 arXiv: 1903.11917

121.

Amin A. Khosravi, Antonio M. Peralta, H.R. Ebrahimi Vishki, Aron-Berner extensions of triple maps with application to the bidual of JB-triple systems, Linear Algebra and its Applications 580 (2019) 436-463. arXiv:1901.01822v1

120.

N.K. Jana, A.K. Karn, A.M. Peralta, Contractive linear preservers of absolutely compatible pairs between C*-algebras, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. RACSAM (2019) 113: 2731-2744. https://doi.org/10.1007/s13398-019-00653-0 arXiv:1810.10886v1

119.

N.K. Jana, A.K. Karn, A.M. Peralta, Absolutely compatible pairs in a von Neumann algebra, Electronic Journal of Linear Algebra 35 (2019), 599-618. https://doi.org/10.13001/1081-3810.3921 arXiv:1801.01216v1

118.

A.M. Peralta, On the unit sphere of positive operators, Banach Journal of Mathematical Analysis 13, no. 1, 91-112 (2019). arXiv:1711.05652v1

117.

A.M. Peralta, Extending surjective isometries defined on the unit sphere of  $\ell_\infty(\Gamma)$, Revista Matemática Complutense 32, no. 1, 99-114 (2019). DOI: 10.1007/s13163-018-0269-2arXiv:1709.09584v1

116.

A. Jiménez-Vargas, A. Morales-Campoy, A.M. Peralta, and M.I. Ramírez, The Mazur-Ulam property for the space of complex null sequences, Linear and Multilinear Algebra 67, no. 4, 799-816 (2019). https://doi.org/10.1080/03081087.2018.1433625 arXiv:1708.08538v2

115.

L. Li, A.M. Peralta, L. Wang, Y.-S. Wang, Weak-2-local isometries on uniform algebras and Lipschitz algebras, Publicacions Matemàtiques 63, no. 1, 241-264 (2019). arXiv:1705.03619v1

114.

M.J. Burgos, J. Cabello-Sánchez, A.M. Peralta, Linear maps between C*-algebras that are *-homomorphisms at a fixed point, Quaestiones Mathematicae 42, no. 2, 151-164 (2019). https://doi.org/10.2989/16073606.2018.1442373 arXiv:1609.07776v1

113.

A.M. Peralta, R. Tanaka, A solution to Tingley’s problem for isometries between unit spheres of compact C*-algebras and JB*-triples, Sci. China Math. 62, no. 3, 553-568 (2019). https://doi.org/10.1007/s11425-017-9188-6

112.

A.M. Peralta, The $\lambda$-function in the space of trace class operators, Mediterr. J. Math. 15:217 (2018). https://doi.org/10.1007/s00009-018-1260-3 arXiv:1804.01303.

111.

A.M. Peralta, Characterizing projections among positive operators in the unit sphere, Adv. Oper. Theory 3 (2018), no. 3, 731-744.

110.

A.M. Peralta, A survey on Tingley’s problem for operator algebras, Acta Sci. Math. (Szeged) 84 (2018), 81-123.

109.

A.B.A. Essaleh, A.M. Peralta, Preservers of λ-Aluthge transforms, Linear Algebra and its Applications 554, 86-119 (2018). DOI: https://doi.org/10.1016/j.laa.2018.05.020 arXiv:1712.07499v1

108.

F.J. Fernández-Polo, A.M. Peralta, On the extension of isometries between the unit spheres of von Neumann algebras, J. Math. Anal. Appl. 466 (2018), 127-143. https://doi.org/10.1016/j.jmaa.2018.05.062

107.

A. Jiménez-Vargas, L. Li, A.M. Peralta, L. Wang, Y.-S. Wang, 2-local standard isometries on vector-valued Lipschitz function spaces, J. Math. Anal. Appl. 461 (2018), no. 2, 1287-1298. arXiv:1708.02897v1

106.

A.B.A. Essaleh, A.M. Peralta, Linear maps on C*-algebras which are derivations or triple derivations at a point, Linear Algebra Appl. 538 (2018), 1-21. https://doi.org/10.1016/j.laa.2017.10.009. arXiv:1706.08326v1

105.

A.B.A. Essaleh, A.M. Peralta, M.I. Ramírez, Pointwise-generalized-inverses of linear maps between C*-algebras and JB*-triples, Operators and Matrices 12 (2018), no. 2, 369-391. doi:10.7153/oam-2018-12-24 \ arXiv:1703.10560v1

104.

F.J. Fernández-Polo, A.M. Peralta, On the extension of isometries between the unit spheres of a C*-algebra and B(H), Trans. Amer. Math. Soc. 5 (2018), 63-80. arXiv:1701.02916v1

103.

F.J. Fernández-Polo, A.M. Peralta, Low rank compact operators and Tingley’s problem, Advances in Mathematics 338 (2018) 1-40.

102.

M. Bohata, J. Hamhalter, O. Kalenda, A.M. Peralta, H. Pfitzner, Preduals of JBW*-triples are 1-Plichko spaces, Quart. J. Math. (Oxford) 69 (2018), 655-680. doi:10.1093/qmath/hax057, arXiv:1609.00274v2

101.

F.J. Fernández-Polo, A.M. Peralta, Partial Isometries: a survey, Advances in Operator Theory, 3 (2018), no. 1, 87-128.

100.

E. Jordá, A.M. Peralta, Almost inner derivations and weak-2-local derivations on the C*-algebra C0(L,A), Integral Equations Operator Theory 89, Issue 1, 89-110 (2017). DOI 10.1007/s00020-017-2390-x

99.

F.J. Fernández-Polo, A.M. Peralta, Tingley’s problem through the facial structure of an atomic JBW*-triple, J. Math. Anal. Appl. 455 (2017), no. 1, 750-760. arXiv:1701.05112v1

98.

F.J. Fernández-Polo, Jorge J. Garcés, A.M. Peralta, I. Villanueva, Tingley’s problem for spaces of trace class operators, Linear Algebra and its Applications 529 (2017), 294-323. http://dx.doi.org/10.1016/j.laa.2017.04.024 arXiv:1702.07182v1

97.

E. Jordá, A.M. Peralta, Stability of derivations under weak-2-local continuous perturbations, Aequationes Mathematicae 91, 99-114 (2017). DOI 10.1007/s00010-016-0438-7.

96.

A.M. Peralta, Orthogonal forms and orthogonality preservers on real function algebras revisited, Linear and Multilinear Algebra. 65, no. 2, 361-374 (2017). DOI 10.1080/03081087.2016.1186147. arXiv:1511.08420v1.

95.

J.C. Cabello, A.M. Peralta, On a generalized Semrl’s theorem for weak-2-local derivations on B(H), Banach J. Math. Anal. 11 (2017), no. 2, 382-397. DOI: http://dx.doi.org/10.1215/17358787-0000009X arXiv:1511.07987v1.

94.

F.B. Jamjoom, A.M. Peralta, A.A. Siddiqui, H.M. Tahlawi, Inner ideals, compact tripotents and Cebysev subtriples of JB*-triples and C*-algebras, RACSAM 111, 129-138 (2017). DOI: 10.1007/s13398-016-0280-8. arXiv:1507.07186v1

93.

M. Niazi, A.M. Peralta, Weak 2-local derivations on Mn, FILOMAT 31:6 (2017), 1687–1708. DOI 10.2298/FIL1706687N

92.

M.J. Burgos, J.C. Cabello, A.M. Peralta, Weak-local triple derivations on C*-algebras and JB*-triples, Linear Algebra and its Applications 506, 614-627 (2016). http://dx.doi.org/10.1016/j.laa.2016.06.042 arXiv:1604.04417v1

91.

L. Li, E. Nieto, A.M. Peralta, Geometric implications of the M(r,s)-properties and the uniform Kadec-Klee property in JB*-triples, Quart. J. Math. Oxford. 67 (2016), 637-651. doi: 10.1093/qmath/haw036 (online) arXiv:1604.04119v1

90.

A.B.A. Essaleh, A.M. Peralta, M.I. Ramírez, Corrigendum: Weak-local derivations and homomorphisms on C*-algebras, Linear and Multilinear Algebra Vol. 64, No. 5, 1009-1010 (2016). http://dx.doi.org/10.1080/03081087.2016.1142171

89.

J. Hamhalter, K. Kudaybergenov, A.M. Peralta, B. Russo, Boundedness of completely additive measures with application to 2-local triple derivations, Journal of Mathematical Physics 57, 021709-1 –021709-22 (2016). DOI: 10.1063/1.4941988 arXiv:1512.03135v1.

88.

J.C. Cabello, A.M. Peralta, Weak-2-local symmetric maps on C*-algebras, Linear Algebra and its Applications 494, 32-43 (2016). http://dx.doi.org/10.1016/j.laa.2015.12.024.

87.

H. Pfitzner, A.M. Peralta, Weak Banach-Saks Property and Koml'os' theorem for preduals of JBW*-triples, Proc. Amer. Math. Soc. 144, no. 11 (2016), 4723-4731. http://dx.doi.org/10.1090/proc/13250

86.

F.B. Jamjoom, A.M. Peralta, A.A. Siddiqui, H.M. Tahlawi, Extremally rich JB*-triples, Ann. Funct. Anal. 7 (2016), no. 4, 578-592

85.

M. Burgos, A.C. Márquez, A. Morales, A.M. Peralta, Linear maps between C*-algebras preserving extreme points and strongly linear preservers, Banach J. Math. Anal. Volume 10, Number 3 (July 2016), 547-565.

84.

H. Pfitzner, A.M. Peralta, Perturbation of l1 -copies in preduals of JBW*-triples, J. Math. Anal. Appl. 434 (2016), no. 1, 149-170. http://dx.doi.org/10.1016/j.jmaa.2015.08.032

83.

S. Ayupov, K. Kudaybergenov, A.M. Peralta, A survey on local and 2-local derivations on C*- and von Neuman algebras, Contemporary Mathematics, Amer. Math. Soc. Volume 672, 73-126 (2016). http://dx.doi.org/10.1090/conm/672/13462.

82.

A.B.A. Essaleh, A.M. Peralta, M.I. Ramírez, Weak-local derivations and homomorphisms on C*-algebras, Linear and Multilinear Algebra Vol. 64, No. 2 (2016) 169-186. DOI:10.1080/03081087.2015.1028320

81.

A. M. Peralta, L.L. Stachó, von Neumann algebra preduals satisfy the linear biholomorphic property, Math. Scand. 118 (2016), 277-284.

80.

F.J. Fernández Polo, A. Molino, A. M. Peralta, Local triple derivations on real C*-algebras and JB*-triples, Bulletin of the Malaysian Mathematical Sciences Society Volume 39, Issue 3, pp 941-955 (2016). DOI:10.1007/s40840-015-0203-4

79.

M. Niazi, A.M. Peralta, Weak-2-local *-derivations on B(H) are linear *-derivations, Linear Algebra and its Applications 487 (2015), 276-300. DOI 10.1016/j.laa.2015.09.028.

78.

F.B. Jamjoom, A.M. Peralta, A.A. Siddiqui, H.M. Tahlawi, Cebysev subspaces of JBW*-triples, Journal of Inequalities and Applications (2015) 2015:288. DOI 10.1186/s13660-015-0813-2.

77.

H. Pfitzner, A.M. Peralta, The Kadec-Pelczy'nski-Rosenthal subsequence splitting lemma for JBW*-triple preduals, Studia Math. 227, No. 1, 77-95 (2015).

76.

A. Ben Ali Essaleh, M. Niazi, A.M. Peralta, Bilocal *-automorphisms of B(H) satisfying the 3-local property, Arch. Math. 104 (2015), 157-164.

75.

F.B. Jamjoom, A.M. Peralta, A.A. Siddiqui, Jordan weak amenability and orthogonal forms on JB*-algebras, Banach J. Math. Anal. Volume 9, Number 4 (2015), 126-145. doi: 10.15352/bjma/09-4-8

74.

M.J. Burgos, F.J. Fernández Polo, J.J. Garcés, A.M. Peralta, 2-local triple homomorphisms on von Neumann algebras and JBW*-triples, J. Math. Anal. Appl. 426, 43-63 (2015).

73.

F.B. Jamjoom, A.M. Peralta, A.A. Siddiqui, H.M. Tahlawi, Approximation and convex decomposition by extremals and the λ-function in JBW*-triples, Quart. J. Math. Oxford 66 (2) (2015) 583-603. doi:10.1093/qmath/hau036

72.

M.J. Burgos, F.J. Fernández Polo, J.J. Garcés, A.M. Peralta, A Kowalski-Slodkowski theorem for 2-local *-homomorphisms on von Neumann algebras, RACSAM 109, Issue 2 (2015), Page 551-568. DOI 10.1007/s13398-014-0200-8.

71.

A.M. Peralta, A note on 2-local representations of C*-algebras, Operators and Matrices 9, Number 2 (2015), 343-358. doi:10.7153/oam-09-20.

70.

F.J. Fernández Polo, A. M. Peralta and M. Ramírez, A Kadec-Pelczynski dichotomy-type theorem for preduals of JBW*-algebras, Israel J. Math. 208 (2015), 45-78. DOI: 10.1007/s11856-015-1193-5.

69.

A.M. Peralta, Positive definite hermitian mappings associated to tripotent elements, Expositiones Mathematicae 33 (2015) 252-258.

68.

K. Kudaybergenov, T. Oikhberg, A.M. Peralta, and B. Russo, 2-local triple derivations on von Neumann algebras, Illinois J. Math. 58, Number 4, Winter 2014, Pages 1055-1069. S 0019-2082.

67.

M. Burgos, F.J. Fernández Polo and A.M. Peralta, Local triple derivations on JB*-triples and C*-algebras, Bull. London Math. Soc. 46 (4), 709-724 (2014).

66.

A.M. Peralta, Chi-Keung Ng, Ngai-Ching Wong, and Jen-Chih Yao, Preserver Problems on Function Spaces, Operator Algebras, and Related Topics [Editorial], Abstract and Applied Analysis Volume 2014, Article ID 723685, 2 pages http://dx.doi.org/10.1155/2014/723685.

65.

J. Garcés, A. M. Peralta, Orthogonal forms and orthogonality preservers on real function algebras, Linear and Multilinear Algebra 62, no. 3, 275-296 (2014). (DOI:10.1080/03081087.2013.772998).

64.

M. Apazoglou and A. M. Peralta, Linear isometries between real JB*-triples and C*-algebras, Quart. J. Math. Oxford 65, 485-503 (2014). (doi:10.1093/qmath/hat033).

63.

M. Burgos, F.J. Fernández Polo, J. Garcés, and A. M. Peralta, Local triple derivations on C*-algebras, Communications in Algebra 42, 1276-1286 (2014).

62.

B. Russo and A. M. Peralta, Automatic continuity of triple derivations on C*-algebras and JB*-triples, Journal of Algebra 399, 960-977 (2014).

61.

J.J. Garcés, A. M. Peralta, D. Puglisi, M.I. Ramírez,, Orthogonally additive, orthogonality preserving, holomorphic mappings between C*-algebras, Abstract and Applied Analysis Volume 2013, Article ID 415354, 9 pages http://dx.doi.org/10.1155/2013/415354.

60.

T. Oikhberg, A. M. Peralta, Automatic continuity of orthogonality preservers on a non-commutative Lp(τ)-space, Journal of Functional Analysis 264, no. 8, 1848-1872 (2013).

59.

J. Garcés and A. M. Peralta, Generalised triple homomorphisms and Derivations, The Canadian Journal of Mathematics 65, no. 4, 783-807 (2013).

58.

T. Ho, A. M. Peralta and B. Russo, Ternary weakly amenable C*-algebras and JB*-triples, Quart. J. Math. Oxford 64, 1109-1139 (2013). (doi:10.1093/qmath/has032).

57.

T. Oikhberg, A. M. Peralta and D. Puglisi, Automatic continuity of $L$-norms on the predual of a von Neumann algebra, Revista Matemática Complutense (Springer) 26, 57-88 (2013).

56.

Antonio M. Peralta and Daniele Puglisi, Orthogonally Additive Holomorphic functions on C*-algebras, Operators and Matrices 6, Number 3, 621-629 (2012).

55.

F.J. Fernández-Polo, J. Martínez, and A. M. Peralta, Contractive Perturbations in JB*-triples, J. London Math. Soc. (2) 85, 349-364 (2012).

54.

F.J. Fernández-Polo, J. Garcés, and A. M. Peralta,Weakly compact orthogonality preservers on C*-algebras, Math. Z. 270, 709-723 (2012).

53.

F.J. Fernández-Polo, J. Garcés, and A. M. Peralta, A Kaplansky Theorem for JB*-triples, Proc. Amer. Math. Soc. 140 3179-3191 (2012).

52.

T. Oikhberg, A. M. Peralta and M. Ramírez, Automatic continuity of M-norms on C*-algebras, J. Mathematical Analysis and Applications 381, 799–811 (2011).

51.

M. Burgos, J. Garcés, and A. M. Peralta, Automatic continuity of biorthogonality preservers between weakly compact JB*-triples and atomic JBW*-triples, Studia Mathematica 204, no. 2, 97-121 (2011).

50.

Peralta, A. M., Una revisión de la propiedad de Dunford-Pettis en productos tensoriales proyectivos de espacios de Banach, Publicaciones del Dpto. de Análisis Matemático, UCM, Sección 1; Núm. 77, 125-132 (2011).

49.

M. Burgos, J. Garcés, and A. M. Peralta, Automatic continuity of biorthogonality preservers between compact C*-algebras and von Neumann algebras, J. Mathematical Analysis and Applications 376, 221-230 (2011).

48.

Diestel, J., Peralta, A.M., Puglisi, D., Sequential w-right continuity and summing operators, Math. Nachr. 284, No. 5-6, 664-680 (2011).

47.

M. Burgos, A. M. Peralta, M. Ramirez, M. E. Ruiz, von Neumann regularity in Jordan-Banach triples, Proceedings of Jordan structures in Algebra and Analysis Meeting. Tribute to El Amin Kaidi for his 60th birthday. Almería, 20, 21 y 22 de Mayo de 2009, Edited by J. Carmona et al., Editorial Círculo Rojo, 2010. ISBN 978-84-92849-51-2 Depósito legal SE-1844-201.

46.

Fernández-Polo, F. J. and Peralta, A. M., Non-commutative generalisations of Urysohn's lemma and hereditary inner ideals, Journal of Functional Analysis 259 (2010) 343–358.

45.

Fernández-Polo, F. J. and Peralta, A. M., On the facial structure of the unit ball in the dual space of a JB*-triple, Mathematische Annalen 348, 1019–1032 (2010).

44.

Peralta, A. M., Villanueva, I., Wright, J.D.M. and Ylinen, Weakly compact operators and the strong* topology for a Banach space, Proc. Roy. Soc. Edinburgh 140 A, 1249-1267 (2010).

43.

Peralta, A. M., Villanueva, I., Wright, J.D.M. and Ylinen K., Quasi Completely continuous multilinear operators, Proceedings of the Royal Society of Edinburgh 140 A (3), 635-649 (2010).

42.

Edwards, C.M., Fernández Polo, F.J., Hoskin, C.S., Peralta, A.M., On the facial structure of the unit ball in a JB*-triple, J. reine angew. Math. 641 (2010), 123-144.

41.

Fernández-Polo, F. J. and Peralta, A. M., A short proof of a Theorem of Pfiztner, Quarterly Journal of Mathematics Oxford 61, 329-336 (2010).

40.

Burgos, M., Fernández Polo, F. J., Garcés, and Peralta, A. M., Orthogonality preservers Revisited, Asian-European Journal of Mathematics Vol. 2, No. 3 (2009) 387-405.

39.

Fernández-Polo, F. J. and Peralta, A. M., Weak compactness in the dual space of a JB*-triple is commutatively determined, Math. Scand. 105, 307–319 (2009).

38.

Palazuelos, C., Peralta, A. M. and Villanueva, I., Factorizing multilinear operators on Banach spaces and C*-algebras, Studia Mathematica 192 (2), 129-146 (2009).

37.

Burgos M. and Peralta, A. M., Conorm and essential conorm in C*-algebras, Integral Equations and Operator Theory 63, 1-16 (2009).

36.

Burgos, M., Fernández Polo, F. J., Garcés, J., Martínez, J. and Peralta, A. M., Orthogonally preservers in C*-algebras, JB*-algebras and JB*-triples, J. Mathematical Analysis and Applications 348 (2008) 220–233.

35.

Palazuelos, C., Peralta, A. M. and Villanueva, I., Orthogonally Additive Polynomials on C*-algebras, Quarterly Journal of Mathematics 59, 363–374 (2008).

34.

M. Burgos, A. Kaidi, A. Morales, A. M. Peralta and M. Ramírez, von Neumann regularity and quadratic conorms in JB*-triples and C*-algebras, Acta Mathematica Sinica 24, No. 2, 185-200 (2008).

33.

Peralta, A. M., Topological characterisation of weakly compact operators revisited, Extracta Mathematicae 22(2), 215-223 (2007).

32.

Bunce, L. J. y Peralta, A. M., Dunford-Pettis properties, Hilbert spaces and projective tensor products, Journal of Functional Analysis 253, 692-710 (2007).

31.

Peralta, A. M., Villanueva, I., Wright, J.D.M. and Ylinen, Topological characterisation of weakly compact operators, J. Mathematical Analysis and Applications 325, 968-974 (2007).

30.

Fernández-Polo, F. J. y Peralta, A. M., Compact tripotents and the Stone-Weierstrass Theorem for C*-algebras and JB*-triples, J. Operator Theory 58:1, 157-173 (2007).

29.

Peralta, A. M., Villanueva, I., Wright, J.D.M. and Ylinen, The Strong*-topology and quasi completely continuous operators on Banach spaces, preprint 2006.

28.

Fernández-Polo, F. J. y Peralta, A. M., Closed tripotents and weak compactness in the dual space of a JB*-triple, J. London Math. Soc. 74 (2006), 75-92.

27.

Peralta, A. M. y Villanueva, I., The alternative Dunford-Pettis on projective tensor products, Math. Z. 252 (2006), 883-897.

26.

Bunce, L. J., Fernández-Polo, F. J., Martínez Moreno, J. and Peralta, A. M., A Saitô-Tomita-Lusin Theorem for JB*-triples and Applications, Quarterly Journal of Mathematics Oxford 57 (2006), 37–48;

25.

Peralta, A. M., Some remarks on weak compactness in the dual space of a JB*-triple, Tohoku Math. J. 58 (2006), 149-159.

24.

Acosta, M. D. y Peralta, A. M., The alternative Dunford-Pettis property for subspaces of the compact operator, Positivity 10, 51-63 (2006).

23.

Becerra Guerrero, J. y Peralta, A. M., The Dunford-Pettis and the Kadec-Klee properties on tensor products of JB*-triples, Math. Z. 251 (2005), no. 1, 117--130.

22.

Bunce, L. J. y Peralta, A. M., Spin spaces and positive decomposition of linear maps on ordered Banach spaces. Quarterly Journal of Mathematics 56, 43-52 (2005).

21.

Peralta, A. M., Avances recientes sobre la propiedad de Dunford-Pettis alternativa para C*-algebras y JB*-triples. Actas del Colloquium del Departamento de Análisis Matemático de la Universidad Complutense de Madrid 63, 55-68 (2005).

20.

Peralta, A. M., New advances on the Grothendieck's inequality problem for bilinear forms on JB*-Triples. Math Inequal Appl. 8, No. 1, 7-21 (2005).

19.

Bunce, L. J. y Peralta, A. M., The alternative Dunford-Pettis property, conjugations and real forms of C*-Algebras, Journal of the London Mathematical Society 71, 161-171 (2005).

18.

Fernández-Polo, F. J., Martínez Moreno, J. y Peralta, A. M., Surjective isometries between real JB*-triples. Mathematical Proceedings of the Cambridge Philosophical Society 137 709-723 (2004).

17.

Fernández-Polo, F. J., Martínez Moreno, J. y Peralta, A. M., Geometric characterization of tripotents in real and complex JB*-triples. Journal of Mathematical Analysis and Applications 295, 435-443 (2004).

16.

Bunce, L. J. y Peralta, A. M., On weak sequential convergence in JB*-triple duals, Studia Mathematica 160 (2), 117-127, (2004).

15.

Becerra Guerrero, J., López, G., Peralta, A. M. y Rodríguez Palacios, A., Relatively weakly open sets in closed balls of Banach spaces, and real JB*-Triples of finite rank. Mathematische Annalen 330, 45-58 (2004).

14.

Becerra Guerrero, J. y Peralta, A. M., Subdifferentiability of the norm and the Banach-Stone theorem for real and complex JB*-Triples, Manuscripta Mathematica 114, no. 4, 503-516 (2004).

13.

Peralta, A. M., On the axiomatic definition of real JB*-triples, Mathematische Nachrichten 256, 100-106, (2003).

12.

Bunce, L. J. y Peralta, A. M., The alternative Dunford-Pettis property in C*-algebras and Von Neumann preduals, Proc. Amer. Math. Soc. 131, n. 4, 1251-1255, (2003).

11.

Bunce, L. J. y Peralta, A. M., Images of contractive projections on operators álgebras, J. Math. Analysis and Applications 272, n. 1, 55-56, (2002).

10.

Ho, T., Martínez Moreno, J., Peralta, A. M. y Russo, B., Derivations on real and complex JB*-triples, J. London Math. Soc. 65, 85-102 (2002).

9.

Peralta, A. M., On summing operators on JB*-triples, Manuscripta Math. 105, 265-281 (2001).

8.

Peralta, A. M. y Rodríguez Palacios, A., Grothendieck's inequalities revisited. Recent progress in Functional Analysis, Proceedings of the International Functional Analysis Meeting on the Occasion of the 70th Birthday of Professor Manuel Valdivia, Valencia, Spain, July 3-7, 2000, (ed. by K.D. Bierstedt, J. Bonet, M. Maestre, J. Schmets), 409-423, North-Holland 2001.

7.

Peralta, A. M. y Rodríguez Palacios, A., Grothendieck's inequalities for real and complex JBW*-triples, Proc. London Math. Soc. 83, 605-625 (2001).

6.

Peralta, A. M., Little Grothendieck's theorem for real JB*-triples, Math. Z., 237, 531-545 (2001).

5.

Peralta, A.M., sobre JB*-triples reales. ISBN 84-338-2746-4, 2001, Servicio Publicaciones de Univ. de Granada (Tesis Doctoral).

4.

Martín, M. y Peralta, A. M., The alternative Dunford-Pettis property in the predual of a Von Neumann algebra, Studia Math. 147, 197-200 (2001).

3.

Acosta, M. D. y Peralta, A. M., An alternative Dunford-Pettis property for JB*-triples, Quartely J. Math 52, 391-401 (2001).

2.

Peralta, A. M. y Stacho, L. L., Atomic decomposition of real JB*-triples, Quarterly J. Math. 52, 79-87 (2001).

1.

Martínez Moreno, J. y Peralta, A. M., Separate weak*-continuity of the triple product in dual real JB*-triples, Math. Z. 234, 635-646 (2000).

Ph. D. Students :

Mathematics Genealogy Project

  • Doctorant: Francisco J. Fernández Polo
  • Títle: Aspectos geométricos en la teoría de los JB*-triples reales y complejos.
  • Degree: Sobresaliente cum Laude (25/06/2004).
  • Supervisers: J. Martínez Moreno y A. M. Peralta
  • Doctorant: Jorge J. Garcés Pérez
  • Títle: Operadores que preservan ortogonalidad y homomorfismos ternarios
  • Degree: Sobresaliente cum Laude (2/07/2013).
  • Superviser: A. M. Peralta
  • Doctorant: Ahlem Ben Ali Essaleh
  • Títle: New classes of local derivations and *-automorphisms on C*-algebras. Faculté des sciences de Monastir. University of Monastir, Tunisia.
  • Degree: Cum Laude (6/05/2016).
  • Superviser: A. M. Peralta, Co-supervised with Prof. Haïkel Skhiri (University of Monastir, Tunisia).

  • Doctorant: María de Nazaret Cueto Avellaneda
  • Títle: Extension of isometries and the Mazur--Ulam property. Universidad de Almería.
  • Degree: Sobresaliente cum Laude (11/09/2020).
  • Superviser: A. M. Peralta

Conferences:

  • Antonio M. Peralta, Conferencia: Separate Weak*-continuity of the triple product in real JB*-triples (trabajo conjunto con J. Martínez), Banach Algebras 99, Pomona, Los Angeles, EE.UU. (1999).
  • Antonio M. Peralta, Conferencia: Little Grothendieck’s Theorem for real JB*-triples, Congreso RSME2000 de la Real Sociedad Matemática Española. Madrid (2000).
  • Antonio M. Peralta, Conferencia: Grothendieck’s inequalities for real and complex JBW*-triples (realizado conjuntamente con Angel Rodríguez), Conference Functional Analysis Valencia 2000, Valencia (2000).
  • Antonio M. Peralta, Conferencia: Grothendieck’s inequalities for real and complex JBW*-triples (realizado conjuntamente con Angel Rodríıguez), “Jordan-Algebren”, Mathematisches Forschungsintitut Oberwolfach, Germany (2000).
  • Antonio M. Peralta y J. Martínez, Conferencia: Separate weak*-continuity of the triple product in dual real JB*-triples,“Jordan-Algebren”,Mathematisches Forschungsintitut Oberwolfach, Germany.(2000).
  • Antonio M. Peralta, Conferencia: On the alternative Dunford-Pettis property in von Neumann algebras andJBW*-triples, Jordan Structures in Analysis, 2001, University College Dublin. Dublin (2001).
  • Antonio M. Peralta, Conferencia: On the axiomatic definition of real JB*-triples, InternationalConference on Jordan Structures 2002, Málaga (2002).
  • Antonio M. Peralta, Conferencia: On weak sequential convergence in JB*-triples and duals, Jordan-BanachTriple Systems, Granada (2002).
  • Antonio M. Peralta, Conferencia: Geometric Characterizations of tripotents in JB*-triples, Jordan-BanachTriple Systems, Santiago 2003.
  • Antonio M. Peralta, Conferencia: New advances on the Grothendieck’s inequality for bilinear forms onJB*-triples, Primer Congreso Conjunto de Matemáticas RSME-SCM-SEIO-SEMA, MAT.ES 2005, Valencia (2005).
  • Antonio M. Peralta, Conferencia: The alternative Dunford-Pettis and the Kadec-Klee properties forJB*-triples and C*-algebras, International Mediterranean Congress of Mathematics, Almería, June 2005.
  • Antonio M. Peralta, Conferencia: A substitute for topology in JB*-triples, Jornada Hispano-Magrebí deAnálisis Funcional y Estructuras no Asociativas, Almería, Noviembre 2005.
  • Antonio M. Peralta, Conferencia: A substitute for topology in JB*-triples, Workshop on Jordan Structuresin Analysis and Geometry 2006, Kauhsiung, Taiwan, April 2006 (picture).
  • Antonio M. Peralta, Conferencia: The Strong* Topology and Quasi Completely Continuous MultilinearOperators, XII Meeting on Real Analysis and Measure Theory, Ischia, Italy, July 2006.
  • Antonio M. Peralta, Conferencia: The Strong*-topology and quasi completely continuous
    multilinear operators on Banach spaces, VI Banach space theory:Classical topics and new
    directions, Satellite Conference ICM, Cáceres, September 2006.
  • Antonio M. Peralta, Operadores que preservan ortogonalidad y aplicaciones ortogonalmente aditivassobre C*-álgebras y JB*-triples, IV Encuentro de Análisis Funcional y Aplicaciones (Red Temática deAnálisis Funcional y Aplicaciones). Salobreña, Abril 2008 (02/04/08-05/04/08).
  • Antonio M. Peralta, Orthogonality preserver and orthogonally additive mappings betweenC*-algebras and JB*-triples, In Jordan structures: nonassociative analysis and geometry 2008, Queen Mary College, University of London.September 2008 (picture).
  • Antonio M. Peralta, Caras norma cerradas en la bola unidad de un JB*-triple (spanish), IVReunión de Coordinación del Proyecto de Excelencia: Aproximación-Algebraico-Analítica de los Sistemas no asociativos y susaplicaciones, FQM 3737. Lanjarón (Granada), 18-20 de Abril de 2009.
  • Antonio M. Peralta, Conormas cuadráticas en C*-álgebras y JB*-triples (spanish),Estructuras de Jordan en Algebra y Analisis. Homenaje al profesor Amin Kaidi por su sesenta cumpleaños. Almería, 20-22 de Mayo de 2009.
  • Antonio M. Peralta, Sequential right continuity and weakly compact operators. Informal Analysis Seminar Dedicated To The Work of Joe Diestel. Kent State University, Kent, Ohio, USA. March 20-21, 2010.
  • Antonio M. Peralta, Right-norm and strong*-norm continuous polynomials and holomorphicmappings. AMS 2010 Spring Southeastern Sectional Meeting, Special Session on Multivariate and Banach Space Polynomials. Lexington University. Lexington, Kentuky, USA. March 27-28, 2010.
  • Antonio M. Peralta, Automatic continuity of biorthogonality preservers on von Neumannalgebras, International Functional Analysis Meeting in Valencia on the Occasion of the 80th Birthday of Professor Manuel Valdivia.Valencia, España, June 7-11, 2010.
  • Antonio M. Peralta, Orthogonality preservers between C*-algebras, School and Workshop on Topics in operator algebras and some applications, Organized by IMI -Interdisciplinary Mathematical Institute, Universidad Complutense de Madrid, Universitat Autònoma de Barcelona, Universidad Carlos III de Madrid, and i-math. Madrid, September 13-17, 2010.
  • Antonio M. Peralta, Weakly Compact Orthogonality Preservers, Workshop on Jordan Structures in Algebra and Analysis 2, Lanjarón, Granada, España, September 30, October 2, 2010.
  • Antonio M. Peralta, Orthogonally Additive Holomorphic functions on C*-algebras and non-commutative measure theory, Integration, Vector Measures and Related Topics IV, Dedicated to Joe Diestel, La Manga, Murcia, March 2 - March 5, 2011.
  • Antonio M. Peralta, M-norms on C*-algebras, V International Course of Mathematical Analysis inAndalusia Almería, September 12-16, 2011 (picture).
  • Antonio M. Peralta, Orthogonality Preservers and M-norms on C*-algebras, International Conference on Jordan Theory, Analysis and Related Topics, InCelebration of the 65th Birthday of Professor Cho-Ho Chu April 30 to May 4, 2012. (picture1, picture2, picture3, picture4, picture5, picture6).
  • Antonio M. Peralta, Weak Compactness in dual spaces of C*-algebras and JB*-triples, Terceras Jornadas de Análisis Matemático en Alicante, 30, 31 de Mayo y1 de Junio 2012. Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Alicante.
  • Antonio M. Peralta, Orthogonal forms and orthogonality preservers on real C*-algebras, International Conference on Operator Theory and Applications. Organized by the Functional Analisys teams of University Mohammed I, Laboratory ofFunctional Analysis, Geometry and Applications (Morocco), and University Lille 1 (France), Oujda, Morocco, from 14 to 19 December 2012 (webpage http://mathinfo-fso.ump.ma/citoa/). Talk . Some Photos.
  • Antonio M. Peralta, M-norms and L-norms on C*-algebras and their dual spaces, Congreso de la Real Sociedad Matemática Española, Santiago de Compostela, 21-25 de Enero, 2013 (talk).
  • Antonio M. Peralta, When orthogonality relations determine the geometric C*-structure of a C*-algebra, IX Encuentro de Análisis Funcional y Aplicaciones (Red Temática de Análisis Funcional y Aplicaciones). Zafra (Badajoz), Spain. April 11-13, 2013. (talk).
  • Antonio M. Peralta, Dunford-Pettis properties in projective tensor products, Workshop on Functional Analysis Valencia 2013 on the occasion of the 60th birthdayof Andreas Defant, Valencia from the 3th to the 6th of June 2013 (talk).
  • Antonio M. Peralta, Holomorphic Functions Between C*-algebras: Conditions To Find Power SeriesExpansions, XII Encuentros de Análisis Funcional Murcia Valencia. Alcoi, Alicante 17-18 Octubre 2013.
  • Antonio M. Peralta, 2-local *-homomorphisms on von Neumann algebras, USA-Uzbekistan Conference onAnalysis and Mathematical Physics. May 20-23, 2014, California State University, Fullerton, California, USA.
  • Antonio M. Peralta, Local derivations: the shift from the associative theory of Kadison and Johnson to Jordan triple scene, Jordan Geometric Analysis and applications, Queen Mary, University of London, London, September 2014 (September 3-5, 2014).
  • Antonio M. Peralta, The λ-function of Aron and Lohman on Jordan structures. XIII encuentro deAnálisis Funcional Murcia-Valencia. Universidad de Valencia. Valencia, Diciembre, 11-13, 2014.
  • Antonio M. Peralta, 2-Local *-Homomorphisms on von Neumann algebras and the Kowalski and Slodkowski Theorem, Invited talk. Special Session Operator algebras. First joint meeting Brazil-Spain in Mathematics. SBM-SBMAC-RSME. Universidade Federal do Ceará, Fortaleza, Brazil. December 7-10, 2015. http://www.sbm.org.br/jointmeeting-spain/
  • Antonio Peralta, Additivity of 2-local and weak-2-local maps on C*-algebras, Invited talk at the Special session Functional Analysis. Second joint Conference of the Belgian, Royal Spanish and Luxembourg Mathematical Societies. Logroño (La Rioja), Spain, June 6-8, 2016.
  • Antonio Peralta, Weak-2-local maps on C*-algebras, Invited talk in the Mini-symposium “Recent Developments in Non-linear Preservers”. 20th Conference of the International Linear Algebra Society (ILAS). Leuven, Belgium, at the KU Leuven. July 11-15,
    2016
  • Antonio Peralta, Tingley’s problem for compact operators. Invited plenary talk. Workshop on Complex Analysis and Operator Theory. IUMPA, Valencia, October, 27-29, 2016.
  • Antonio M. Peralta, Jordan techniques to solve Tingley’s problem in the case of compact operators. Conference: Preservers Everywhere 19-23 June 2017. Bolyai Institute, University of Szeged, Szeged, Hungary. Hungarian Academy of Sciences, the University of Szeged and the Hungarian National Research, Development and Innovation Office.
  • Antonio Peralta, New progresses on Tingley's problem for C*-algebras. Workshop on Complex Analysis and Operator Theory, Universidad Politécnica de Valencia, September, 18-22, 2017.
  • Antonio Peralta, On the chances to extend a surjective isometry between the unit spheres of two operator algebras. Conference Non-linear Functional Analysis. Universidad Politécnica de Valencia, October, 17-20, 2017.
  • Antonio Peralta, Spherical variants of the Gleason-Kahane-Zelazko and Kowalski-Slodkowski. Invited talk. Workshop on infinite dimensional analysis 2018 on the occasion of the 60th birthday of Domingo García Valencia, 1-3/02/2018. Facultad de Matemáticas. Universitat de Valencia.
  • Antonio Peralta, Can one determine the structure of a von Neumann algebra by the λ-Aluthge transform?. Invited talk. Workshop on the frontiers between Functional Analysis and Algebra (WFFAA) A tribute to Prof. Amin Kaidi on the occasion of his retirement. Department of Mathematics. University of Almería, September 13-14, 2018.
  • Antonio Peralta, Preservers of λ-Aluthge transforms on products. Invited talk. Preserver Weekend in Szeged, Bolyai Institute, University of Szeged, Szeged, Hungary, 12-14 April 2019.
  • Antonio Peralta, Markushevich bases and projectional skeletons for JBW*-triple preduals. Invited talk. AGA, Analysis, Geometry and Algebra. Trinity College Dublin and UCD. May 8-10, 2019.
  •  Antonio Peralta, Tingley’s problem for subsets strictly smaller than the unit sphere. Invited talk. “Preserver Webinar” together with Reading University Analysis Seminar. Reading, UK (online webinar). June 12th, 2020.
  • Antonio M. Peralta, Spinning the Gleason-Kahane-Zelazko and Kowalski-Slodkowski theorems. Invited talk. Zagreb Workshop on Operator Theory 2020. June 29-30, 2020. University of Zagreb, Croatia.
  • Antonio M. Peralta, Linear maps which are (triple) derivable or antiderivable at a point. Invited talk in the Mini-symposium ``Recent Developments on Preservers''. 8th European Congress of Mathematics - 8ECM, 20--26 June 2021. Portoroz, Slovenia. University of Primorska, Andrej Marusic Institute (UP IAM), University of Ljubljana, University of Maribor, Institute of Mathematics, Physics and Mechanics, The Society of Mathematicians, Physicists and Astronomers, Slovenia and Slovenian Discrete and Applied Mathematics Society (SDAMS).
  • Antonio M. Peralta, Wigner–Uhlhorn type theorems for bijective transformations between sets of minimal tripotents. Invited talk in the Workshop “Research on preserver problems on Banach algebras and related topics” (Homepage: https://www.smartchair.jp/hp/PPBA2021) 25 - 27 October, 2021. RIMS, Kyoto (Online). RIMS (Research Institute for Mathematical Sciences), Kyoto
  • Antonio M. Peralta, Invertible elements as metric invariants in Banach and Jordan-Banach algebras. Plenary talk. The International Online Conference “Current Trends in Abstract and Applied Analysis” May 12–15, 2022, Ivano-Frankivsk, Ukraine. https://conference.pu.if.ua/cta/pages/schedule.php Ivano-Frankivsk Mathematical Society, Ivano- Frankivsk, Ukraine. Online.
    Vasyl Stefanyk Precarpathian National University, V.N. Karazin Kharkiv National University, Kharkiv, Institute of Mathematics of National Academy of Sciences, Kyiv, Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of National Academy of Sciences, Lviv, Oles Honchar Dnipro National University, Dnipro, National Pedagogical Dragomanov University, Kyiv, National University of Life and Environmental Sciences of Ukraine, Kyiv.
  • Antonio M. Peralta, Distance-preserving bijections between sets of invertible elements in unital Jordan-Banach algebras. Invited talk in the Mini-symposium "General Preservers". 24th Conference of the International Linear Algebra Society (ILAS). Galway, Ireland, at the National University of Ireland, Galway. June 20-24, 2022. The International Linear Algebra Society (ILAS).
  • Antonio M. Peralta, Distance-preservers between unitary sets in JB*-algebras. Plenary talk. Conference: Operators on Banach algebras and related topics, 16-17 July, 2022, Tarbiat Modares University (online). Tarbiat Modares University, Tehran, Iran (online). The Faculty of Mathematical Sciences at Tarbiat Modares University.
  • Antonio M. Peralta, New approaches to the Gleason-Kahane-Zelazko and Kowalski-Slodkowski theorems. Invited plenary speaker. 25th conference on "Banach Algebras and Applications 2022" will be held at the University of Granada in Granada, Spain during 18-23, July 2022. Facultad de Ciencias, Departamento de Análisis Matemático, IMAG Instituto de Matemáticas, Universidad de Granada.
  • Antonio M. Peralta, Characterization of multiplicative maps on
    complex Banach algebras in terms of the spectrum    . Invited plenary speaker. International Conference on ``Progress in Functional Analysis: Methods and Applications''. Lecce, September 19-21, 2022. University of Salento, Lecce, Italy. University of Salento, Lecce and University of Catania, Italy.
  • Antonio M. Peralta, Extending surjective isometries from the unit sphere of C*-algebra lacking of extreme points. Invited plenary speaker. First International Days of Complex and Functional Analysis and Spectral Theory and 16th National Meeting of the Network of Spectral Theory and Applications. El Jadida, 24-25 et 26 Novembre 2022. Organized by L'équipe d'Analyse complexe et Fonctionnelle de Laboratoire de Mathématiques Fondamentales de la Faculté des Sciences d'El Jadida, El Jadida, Morocco. El Jadida, Morocco.
  • Antonio M. Peralta, Tingley's problem on the extension of surjective isometries from the unit sphere of a C*-algebra, invited speaker. Workshop. 3rd Barcelona Weekend on Operator Algebras. January 27-28, 2023. CRM Universitat Autònoma de Barcelona.
  • Antonio M. Peralta, Metric spaces associated with invertible elements in unital Jordan--Banach algebras. Invited speaker. VII Non-Associative Day in Lisbon 05/05/2023. Técnico Lisboa - Universidade de Lisboa - CAMGSD (Lisbon, Portugal).
  • Antonio M. Peralta, Wigner's theorem for bijections preserving order and orthogonality between sets of tripotents. Invited plenary speaker. Operator Theory Days
    conference in honor of Mostafa Mbekhta May 24th and 25th, 2023 in Lille. France. Laboratoire Paul Painlevé, Labex CEMPI, Fédération de Recherche Mathématique du Nord Pas de Calais, CNRS, Université de Lille 1, GDR AFHP (Analyse Fonctionnelle, Harmonique et Probabilités) et le Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville.
  • Antonio M. Peralta, Metric invariants for unital Banach and Jordan-Banach algebras. The Spanish-Polish Mathematical Meeting. Uniwersytet Pódzki and Politechnika Pódzka. Lódz, Poland. September 4--8, 2023. Real Sociedad Matemática Española, Sociedad Española de Matemática Aplicada,Societat Catalana de Matemàtiques, and Polskie Towarzystwo Matematyczne.
  • Antonio M. Peralta, On the strict topology of the multiplier algebra of a JB*-algebra. IX Non-Associative Day in Covilhã, 24/11/2023. University of Beira Interior (Covilhã, Portugal).
  • Antonio M. Peralta, Lie-Trotter formulae for Jordan-Banach algebras, XI Non-associative Day in Funchal, 22/03/2024, Funchal, Universidade da Madeira. Funchal, Portugal.
  • Antonio M. Peralta, Cartan factors, tripotents and Wigner's theorem. Parallel Session "Non-associative algebras in Functional Analysis". Encontro Nacional da Sociedade Portuguesa de Matemática (https://enspm2024.spm.pt), Universidade do Minho, em Braga, Portugal, 10 e 12 de julho de 2024. Sociedade Portuguesa de Matemática.
  • Antonio M. Peralta, Surjective isometries between spheres of positive elements in C*-algebras. Mini-Symposium entitled: "MS: Operator Algebras. Slot 2/2. (MS-41)". 9th European Congress of Mathematics, Seville, Spain, from 15th to 19th July, 2024. European Mathematical Society.
  • Antonio M. Peralta, Cartan factors as an ideal mathematical model for Wigner's theorem. Special session "Jordan algebra Structures and Operator theory". IWOTA2024-35th International Workshop on Operator Theory and its Applications, University of Kent, Canterbury, UK, August 12-16, 2024.

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Research Projects:

  • Análisis Funcional y sus aplicaciones FQM-199, Junta de Andalucía (01/01/99--31/12/2010).
    P. I. Dr. Angel Rodríguez Palacios. web
  • Análisis Funcional: Sistemas Triples de Jordan-Banach MTM2005-02541, Ministerio de Educación y Ciencia, (31/12/2005--31/12/2008)
    P.I. Dr. Antonio M. Peralta.
  • Aproximación algebraico-analítica de los sistemas no-asociativos y sus aplicaciones FQM-1215, Proyecto de Excelencia, Junta de Andalucía (01/02/2006--31/01/2009).
    P. I. Dr. Angel Rodríguez Palacios.
  • Functional Analysis: C*-algebras, JB*-triples and Jordan Structures in Analysis, MTM2008-02186. Ministerio de Ciencia e Innovación, (01/01/2009 --31/12/2011)
    P.I. Dr. Antonio M. Peralta.
  • Aproximacion algebraico-analítica de los sistemas noasociativos y sus aplicaciones (Proyecto de Excelencia 2008) FQM-3737 Proyecto de Excelencia, Junta de Andalucía (14/01/2009 -- 13/01/2013).
    P.I. Dr. Angel Rodríguez Palacios.
  • Functional Analysis: C*-algebras and JB*-triples, MTM2011-23843. Ministerio de Ciencia e Innovación, (01/01/2012 --31/12/2014)
    P.I. Dr. Antonio M. Peralta.
  • Técnicas de Análisis Funcional en el estudio de la geometría de las C*-lgebras y las estructuras de Jordan MTM2014-58984-P. Spanish Ministry of Economy and Competitiveness (01/01/2015 -- 31/12/2017)
    P.I.  Dr. Antonio M. Peralta. 
  • Preservers problems via Functional Analysis PGC2018-093332-B-I00. Ministerio de Ciencia, Innovación y Universidades (01/01/2019 -- 31/12/2021)
    P.I. Dr. D. Antonio M. Peralta.
  • Problemas sobre ”preservers”desde la perspectiva del Análisis Funcional A–FQM–242–UGR18. Universidad de Granada, Junta de Andalucía y Unión Europea. Programa Operativo FEDER Andalucia 2014–2020. (01/01/2020--31/12/2021)
    P.I.: Dr. Antonio M. Peralta.
  • Operadores y Geometría de los Espacios de Banach, Interacción y Aplicaciones. PY20_00255. Junta de Andalucía. Consejería de Transformación Económica, Industria, Conocimiento y Universidades. 01/07/2021 -- 31/12/2022. P.I. Dr. D. Antonio M. Peralta. Univ. de Granada.
  • Geometria y operadores en espacios y álgebras de Banach. PID2021-122126NB-C31. Ministerio de Ciencia e Innovación, 01/09/2022 -- 30/08/2026. P.I.'s Dr. D. Martin Suarez, Miguel and Peralta Pereira, Antonio Miguel, Univ. de Granada.
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Invited talks:

  • Reading University, U.K. (22-10-2002). Pure Mathematics Seminar.
  • Colloquium del Departamento de Análisis Matemático de la Universidad Complutense de Madrid (4-12-2003).
  • Reading University, U.K. (26-05-2004). Pure Mathematics Seminar.
  • Colloquium del Departamento de Análisis Matemático de la Universidad Complutense de Madrid (11-11-2004).
  • ``Arbeitsgemeinschaft Komplexe Analysis'' (22-03-2005), Eberhard Karls Universität Tübingen, Mathematisches Institut (Germany).
  • ``Jordan-Banach triple systems, Santiago 2005'' (14/09/2005-18/09/2005), Universidad de Santiago de Compostela.
  • Seminar Of Functional Analysis, Mathematical Institute, Oxford (28/02/2006).
  • Seminario del Departamentode Álgebra y Análisis Matemático de la Universidad de Almería (16/03/2007).
  • Seminario asociado al Programa de Postgrado de Investigación Matemática del Departamento de Análisis Matemático de la Universidad Complutense de Madrid (2008).
  • Seminario del Departamento de Álgebra y Análisis Matemático de la Universidad de Almería (02/03/2009).
  • University Of California, Irvine. Analysis Seminar (March, 12, 2010).
  • Seminario de Estructuras Algebraicas y Análisis Funcional. Departamento de Álgebra y Análisis Matemático de la Universidad de Almería (22/07/2010).
  • Colloquium del Departamento de Análisis Matemático de la Universidad Complutense de Madrid (24-March-2011). Title “Weakly compact orthogonality preservers on C(K)-spaces and C*-algebras”.
  • King Saud University, Riyadh, Saudi Arabia (05-06-2012). Seminar "On the Dieudonne-Grothendieck-Pfitzner Theorem".
  • Departamento de Álgebra y Análisis Matemático de la Universidad de Almería. Conference "Contractive perturbations and weakly compact elements in JB*-triples" (Julio 2012).
  • Queen Mary University of London, U.K. (27-11-2012). Geometry and Analysis Seminar. Title: "On the facial structure of the unit ball of a JB*-triple and its dual space".
  • Reading University, U.K. (30-11-2012). Analysis Seminar. Title: "On the facial structure of the unit ball of a JB*-triple and its dual space".
  • Universita degli Studi di Catania, Italy (22-May-2013). Dipartimento di Matematica e Informatica, Functional Analysis Seminar. Title: "M-norms on C*-algebras".
  • Departamento de Matematicas de la Universidad de Almería. Seminario de Álgebra y Análisis Matemático. Title: "When does a holomorphic function between C*-algebras admit a power series expansion?" (14 de Octubre de 2013).
  • Université Pierre et Marie Curie - Paris 6, Institut de Mathématiques de Jussieu, France (February 20th, 2014). Séminaire d'Initiation a l'Analyse. Title "The interplay between topology and geometry to describe the facial structure of C*-algebras and JB*-triples".
  • Universite d'Orleans, Département de Mathematiques, France (February 21st, 2014). Seminar "JB*-triples: from their origins in Holomorphic theory to the results in Geometry of Banach spaces".
  • Colloquium del Departamento de Análisis Matemático de la Universidad Complutense de Madrid (10-04-2014). “Power series expansions for holomorphic functions between C*-algebras”.
  • King Saud University, Riyadh, Saudi Arabia. Department of Mathematics. Seminar "2-local *-representations on von Neumann algebras and C*-algebras" (Wednesday, April 8th, 2015).
  • Departamento de Matemáticas de la Universidad de Almería. Seminario de Algebra y Análisis Matemático. "2-local maps on C*-algebras. The Kowalski-Slodkowski theorem" (07 de Diciembre de 2015).
  • Instituto Universitario de Matemática Pura y Aplicada(IUMPA), Valencia. "The Kowalski-Slodkowski theorem as a pioneering result in the theory of 2-local automorphisms”. (27 de Mayo de 2016).
  • Departamento de Matemáticas de la Universidad de Almería. "Towards the Kadec-Pe lczynski-Rosenthal subsequence splitting lemma" (28 de Julio de 2015).
  • Colloquium del Departamento de Análisis Matemático de la Universidad Complutense de Madrid (24-11-2016). "On Tingley´s problem for compact operators”.
  • Departamento de Matemáticas de la Universidad de Almería. Seminario de Análisis Matemático. "On the extension of isometries between the unit spheres of two Banach spaces”. Viernes 17 de Marzo de 2017.
  • Tianjin University of Technology, China. "Tingley’s problem for non-commutative C*-algebras". April 19th, 2017.
  • School of Mathematical Sciences, Nankai University, China. "Weak-local and weak-2-local maps on Banach spaces and C*-algebras". April 20th, 2017.
  • Departamento de Matemáticas de la Universidad de Almería. Seminario de Análisis Matemático. Título: "Extensiones de isometrías entre álgebras de operadores". Jueves 20 de Julio de 2017.
  • Escuela de Doctorado de la Universidad de Cádiz. III Jornadas Doctorales del Programa de Doctorado en Matemáticas. 21 y 22 de noviembre de 2017. Título: "El teorema de Mazur-Ulam y la posibilidad de extender isometrías entre subconjuntos de espacios normados."
  • L’Ecole Doctorale CIMPA de Casablanca de (Maroc), Algèbres non associatives. Aspects analytique, géométrique et applications, 06-16 Mars 2018. "New classes of local and 2-local maps on C*-algebras, JB*-algebras, and JB*-triples”.
  • Bolyai Institute at Szeged University in Hungary. Talk in at the Analysis Seminar entitled "New spherical generalizations of the Gleason-Kahane-Zelazko and Kowalski-Slodkowski theorems". October 2nd, 2018.
  • Seminar at the Department of Analysis at Budapest University of Technology and Economics. Seminar entitled "On the extension of isometries". October 3rd, 2018.
  • XX Encuentro Nacional de Estudiantes de Matemáticas (ENEM). Granada 22--27 de Julio de 2019. Charla ``Un problema actual de Análisis Matemático''. 25 de Julio de 2019.
  • Part-time lecturer at the Faculty of Science and Graduate School of Science and Technology, Niigata University, Japan. A course for undergraduate students entitled "Beyond the Mazur-Ulam theorem: what is the smallest part of a Banach space determining the whole structure?" from January 18th to 29th, 2021 (25 hours). A course for graduate students entitled "On the extension of isometries between the unit spheres'" from February 1st to 11th, 2021 (20 hours).
  • Ateneo del Instituto de Investigación en Matemáticas de la Universidad de Valladolid (IMUVa). Conferencia titulada "One sphere to determine all the other structures". Fecha 27 de Mayo de 2021.
  • Wigner-Uhlhorn type theorems for bijective transformations between sets of (minimal) tripotents (I and II). Nankai University, Tianjin, China. September 15 and 22, 2021.
  • “Wigner’s unitary-antiunitary theorem from the eyes of Jordan structures”. Seminario del Dpto. de Matemáticas de la Universidad de Almería. Seminario Emmy Noether, Edificio CITE III, 9 de febrero de 2022.
  • “How can we apply Jordan structures to reinterpret Wigner-Uhlhorn theorem?” LieJor Online Seminar: Algebras, Representations, and Applications. Instituto de Matemática e Estatística da Universidade de Sao Paulo. 31/Mar/2022. Link: https://youtu.be/1R9ojI0SiUk
  • "Bijections preserving distances between sets of invertible elements in unital Banach and Jordan-Banach algebras" Nankai University, Tianjin, China. September 9, 2022.
  • "The Gleason-Kahane-Zelazko Theorem remains in full topicality". Nankai University, Tianjin, China. September 12, 2022.
  • "Seeking a minimal geometric invariant for Banach spaces, C*-algebras and other structures". Operator Algebras Seminar. Federal University of Santa Catarina. Mathematics Department. Florianópolis, Brazil. September 16th, 2022.
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© Copyright 2010 Antonio M. Peralta