Licenciado en Matemáticas en la Universidad de Granada, doctorándose en 1974 con la Tesis “Contribución a la teoría de las C*-álgebras con unidad”. Es profesor de la Universidad de Granada desde 1972 hasta la actualidad, alcanzando la Cátedra de Análisis Matemático en 1986.
Es autor de un centenar y medio de artículos de investigación, entre los que destacan los siguientes:
A. RODRÍGUEZ (1980) "A Vidav-Palmer theorem for Jordan C*-algebras and related topics". Journal of the London Mathematical Society 22, 318-332.
A. RODRÍGUEZ (1983) "Nonassociative normed algebras spanned by hermitian elements". Proceedings of the London Mathematical Society 47, 258-274.
J.F. MENA, R. PAYÁ, and A. RODRíGUEZ (1985) "Semisummands and semiideals in Banach spaces". Israel Journal of Mathematics 51, 33-67.
A. RODRÍGUEZ (1985) "The uniqueness of the complete algebra norm topology in complete normed nonassociative algebras". Journal of Functional Analysis 60, 1-15.
A. RODRÍGUEZ (1990) "Automatic continuity with application to C*-algebras". Mathematical Proceedings of the Cambridge Philosophical Society 107, 345-347.
R. PAYÁ and A. RODRÍGUEZ (1991) "Banach spaces which are semi-L-summands in their biduals". Mathematische Annalen 289, 529-542.
A. FERNÁNDEZ, E. GARCÍA, and A. RODRÍGUEZ (1992) "A Zelmanov prime theorem for JB*-algebras". Journal of the London Mathematical Society 46, 319-335.
A. RODRÍGUEZ (1993) "Properly semi-L-embedded complex spaces". Studia Mathematica 106, 197-202.
A. RODRÍGUEZ, A.M. SLINKO, and E.I. ZELMANOV (1994) "Extending
the norm from Jordan-Banach algebras of hermitian elements to their
associative envelopes". Communications in Algebra 22, 1435-1455.
A. RODRÍGUEZ (1994) "Jordan structures in Analysis". In Jordan algebras, Proceedings of the Conference held in Oberwolfach, Germany, August 9-15, 1992 (Ed. W. Kaup, K. McCrimmon and H.P. Petersson), 97-186, Walter de Gruyter, Berlin-New York.
J.M. ISIDRO, W. KAUP and A. RODRÍGUEZ (1995) "On real forms of JB*-triples". Manuscripta Mathematica 86, 311-335.
M. CABRERA, A. MORENO, A. RODRÍGUEZ and E.I. ZELMANOV (1996) "Jordan polynomials can be analytically recognized". Studia Mathematica 117, 137-147.
A. KAIDI, M.I. RAMÍREZ and A. RODRÍGUEZ (1997) "Absolute-valued
algebraic algebras are finite-dimensional". Journal of Algebra 195, 295-307.
A. MORENO and A. RODRÍGUEZ (2000) "On the Zelmanovian classification of prime JB*-triples". Journal of Algebra 226, 577-613.
A. KAIDI, A. MORALES and A. RODRÍGUEZ (2001) "A holomorphic characterization of C*- and JB*-algebras". Manuscripta Mathematica 104, 467-478.
J. BECERRA, G. LÓPEZ, A.M. PERALTA and A. RODRÍGUEZ (2004)
"Relatively weakly open sets in closed balls of Banach spaces, and real JB*-triples of finite rank". Mathematische Annalen 330, 45-58.
A. RODRÍGUEZ (2004) "Absolute-valued algebras, and absolute-valuable Banach spaces". In Advanced Courses of Mathematical Analysis I, Proceedings of the First International School Cádiz, Spain 22-27 September 2002 (edited by A. Aizpuru-Tomás and F. León-Saavedra), 99-155, World Scientific.
J. BECERRA and A. RODRÍGUEZ (2007) "C*- and JB*-algebras generated by a non self-adjoint idempotent". Journal of Functional Analysis 248, 107-127.
J. BECERRA and A. RODRÍGUEZ (2008) "Banach spaces with the Daugavet property, and the centralizer". Journal of Functional Analysis 254, 2294-2302.
Ha dirigido 19 Tesis Doctorales. Ha sido conferenciante invitado en diferentes congresos, entre los que destacan los siguientes:
- Colloque sur les algèbres de Jordan, Montpellier (Francia), 1985.
- Oberwolfach conference on Jordan algebras, Oberwolfach (Alemania), 1985, 1988, 1992 y 2000.
- FifthWangerooge-meeting on Functional Analysis, Spiekeroog (Alemania), 1990.
- 39-th Banach semester, Varsovia (Polonia), 1995.
- Conference on topological algebras, Varsovia (Polonia), 1995.
- Special sesion on Banach algebras of the annual meeting of the
American Mathematical Society, San Diego (U.S.A.), 1997.
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