Research:

Fields of interest

Publications

Ph. D. Students

Conferences

español

Degrees:

• 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").

Fields of interest:

• 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

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Publications: (in some cases you can download the preprint version of the paper clicking on the title)

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).
2. Peralta, A. M. y Stacho, L. L., Atomic decomposition of real JB*-triples, Quarterly J. Math., 52, 79-87 (2001).
3. Acosta, M. D. y Peralta, A. M., An alternative Dunford-Pettis property for JB*-triples, Quartely J. Math, 52, 391-401 (2001).
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).
5. Peralta, A.M., sobre JB*-triples reales. ISBN 84-338-2746-4, 2001, Servicio Publicaciones de Univ. de Granada (Tesis Doctoral).
6. Peralta, A. M., Little Grothendieck's theorem for real JB*-triples, Math. Z., 237, 531-545 (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).
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.
9. Peralta, A. M., On summing operators on JB*-triples, Manuscripta Math., 105, 265-281 (2001).
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).
11. Bunce, L. J. y Peralta, A. M., Images of contractive projections on operators álgebras, J. Math. Analysis and Applications 272, nº1, 55-56, (2002).
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, nº4, 1251-1255, (2003).
13. Peralta, A. M., On the axiomatic definition of real JB*-triples, Mathematische Nachrichten 256, 100-106, (2003).
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).
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).
16. Bunce, L. J. y Peralta, A. M., On weak sequential convergence in JB*-triple duals, Studia Mathematica, 160 (2), 117-127, (2004).
17. Fernandez-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).
18. Fernandez-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).
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).
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).
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).
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).
23. Acosta, M. D. y Peralta, A. M., The alternative Dunford-Pettis property for subspaces of the compact operators, Positivity 10, 51-63 (2006) .
24. Peralta, A. M., Some remarks on weak compactness in the dual space of a JB*-triple, to appear in Tohoku Math. J. 58 (2006), 149-159;
25. 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.
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;
27. Peralta, A. M., Una revisión de la propiedad de Dunford-Pettis en productos tensoriales proyectivos de espacios de Banach, to appear in Actas del Colloquium del Departamento de Análisis Matemático de la Universidad Complutense de Madrid (2006).
28. Peralta, A. M. and Villanueva, I., The alternative Dunford-Pettis on projective tensor products, Math. Z. 252 (2006), 883-897.
29. Fernández-Polo, F. J. and Peralta, A. M., Compact tripotents and the Stone-Weierstrass Theorem for C*-algebras and JB*-triples, J. Operator Theory, 58:1, 157-173 (2007).
30. 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.
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).
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).
33. Peralta, A. M., Topological characterisation of weakly compact operators revisited, Extracta Mathematicae 22(2), 215-223 (2007).
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).
35. Palazuelos, C., Peralta, A. M. and Villanueva, I., Orthogonally Additive Polynomials on C*-algebras, Quarterly Journal of Mathematics, 59, 363–374 (2008).
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.
37. Burgos M. and Peralta, A. M., Conorm and essential conorm in C*-algebras, Integral Equations and Operator Theory 63, 1-16 (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).
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).
40. 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).
41. 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.
42. C. M. Edwards, F. J. Fernández Polo, C. S. Hoskin, and A. M. Peralta, On the facial structure of the unit ball in a JB*-triple, J. reine angew. Math. 641 (2010), 123-144
43. Joe Diestel, Antonio M. Peralta and Daniele Puglisi, Sequential w-right continuity and summing operators, to appear in Math. Nachr.
44. Peralta, A. M., Villanueva, I., Wright, J.D.M. and Ylinen, Quasi Completely continuous multilinear operators, Proceedings of the Royal Society of Edinburgh 140 A (3), 635-649 (2010).
45. Peralta, A. M., Villanueva, I., Wright, J.D.M. and Ylinen, Weakly compact operators and the strong* topology for a Banach space, to appear in Proc. Roy. Soc. Edinburgh Sect. A.
46. Peralta, A. M., Villanueva, I., Wright, J.D.M. and Ylinen, The Strong*-topology and quasi completely continuous operators on Banach spaces, preprint 2006.
47. Fernández-Polo, F. J. and Peralta, A. M., On the facial structure of the unit ball in the dual space of a JB*-triple, to appear in Mathematische Annalen.
48. 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
49. M. Burgos, J. Garcés, and A. M. Peralta, Automatic continuity of biorthogonality preservers between compact C*-algebras and von Neumann algebras, preprint 2009.
50. 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-1844-2010.
51. M. Burgos, J. Garcés, and A. M. Peralta, Automatic continuity of biorthogonality preservers between weakly compact JB*-triples and atomic JBW*-triples, preprint 2009.
52. F.J. Fernández-Polo, J. Garcés, and A. M. Peralta, A Kaplansky Theorem for JB*-triples, preprint 2010.
53. F.J. Fernández-Polo, J. Garcés, and A. M. Peralta,Weakly compact orthogonality preservers on C*-algebras, preprint 2010.
54. F.J. Fernández-Polo, J. Martínez, and A. M. Peralta, Contractive Perturbations in JB*-triples, preprint 2010.
55. B. Russo and A. M. Peralta, Automatic continuity of triple derivations, preprint 2010.

Cites and reivews in MathSciNet

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Ph. D. Students :

• Francisco J. Fernández Polo

Títle: Aspectos geométricos en la teoría de los JB*-triples reales y complejos

Degree: cum Laude (25/06/2004)

Advisers: J. Martínez Moreno and A. M. Peralta

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Conferences:

• Antonio M. Peralta, Title: Separate Weak*-continuity of the triple product in real JB*-triples (with J. Martínez), Banach Algebras 99, Pomona, Los Angeles, U.S.A. (1999).
• Antonio M. Peralta, Title: Little Grothendieck’s Theorem for real JB*-triples, Congreso RSME2000 de la Real Sociedad Matemática Española. Madrid (2000).
• Antonio M. Peralta, Title: Grothendieck’s inequalities for real and complex JBW*-triples (with Angel Rodríguez), Conference Functional Analysis Valencia 2000, Valencia (2000).
• Antonio M. Peralta, Title: Grothendieck’s inequalities for real and complex JBW*-triples (with Angel Rodríıguez), “Jordan-Algebren”, Mathematisches Forschungsintitut Oberwolfach, Germany (2000).
• Antonio M. Peralta and J. Martínez, Title: Separate weak*-continuity of the triple product in dual real JB*-triples,“Jordan-Algebren”, Mathematisches Forschungsintitut Oberwolfach, Germany.(2000).
• Antonio M. Peralta, Title: On the alternative Dunford-Pettis property in von Neumann algebras and JBW*-triples, Jordan Structures in Analysis, 2001, University College Dublin. Dublin (2001).
• Antonio M. Peralta, Title: On the axiomatic definition of real JB*-triples, International Conference on Jordan Structures 2002, Málaga (2002).
• Antonio M. Peralta, Title: On weak sequential convergence in JB*-triples and duals, Jordan-Banach Triple Systems, Granada (2002).
• Antonio M. Peralta, Title: Geometric Characterizations of tripotents in JB*-triples, Jordan-Banach Triple Systems, Santiago 2003.
• Antonio M. Peralta, Title: New advances on the Grothendieck’s inequality for bilinear forms on JB*-triples, Primer Congreso Conjunto de Matemáticas RSME-SCM-SEIO-SEMA, MAT.ES 2005, Valencia (2005).
• Antonio M. Peralta, Title: The alternative Dunford-Pettis and the Kadec-Klee properties for JB*-triples and C*-algebras, International Mediterranean Congress of Mathematics, Almeríıa 2005.
• Antonio M. Peralta, Title: A substitute for topology in JB*-triples, Jornada Hispano-Magrebí de Análisis Funcional y Estructuras no Asociativas, Almería, Noviembre 2005.
• Antonio M. Peralta, Title: A substitute for topology in JB*-triples, Workshop on Jordan Structures in Analysis and Geometry 2006, Kauhsiung, Taiwan, April 2006 (picture).
• Antonio M. Peralta, Title: The Strong* Topology and Quasi Completely Continuous Multilinear Operators, XII Meeting on Real Analysis and Measure Theory, Ischia, Italy, July 2006.
• Antonio M. Peralta, Title: 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 aditivas sobre C*-álgebras y JB*-triples (spanish), IV Encuentro de Análisis Funcional y Aplicaciones (Red Temática de Análisis Funcional y Aplicaciones). Salobreña, Abril 2008 (02/04/08-05/04/08).
• Antonio M. Peralta, Operadores que preservan ortogonalidad y aplicaciones ortogonalmente aditivas sobre C*-álgebras y JB*-triples (spanish), IV Encuentro de Análisis Funcional y Aplicaciones (Red Temática de Análisis Funcional y Aplicaciones). Salobreña, Abril 2008 (02/04/08-05/04/08).
• Antonio M. Peralta, Orthogonality preserver and orthogonally additive mappings between C*-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), IV Reunión de Coordinación del Proyecto de Excelencia: Aproximación-Algebraico-Analítica de los Sistemas no asociativos y sus aplicaciones, 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 holomorphic mappings. 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 Neumann algebras, International Functional Analysis Meeting in Valencia on the Occasion of the 80th Birthday of Professor Manuel Valdivia.Valencia, Spain, 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.
  

Research Proyects:

• 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.
• Análisis Funcional: C*-algebras, JB*-triples y Estructuras de Jordan en Análisis, 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.

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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).

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