ArticleOriginal scientific text
Title
Jordan polynomials can be analytically recognized
Authors 1, 1, 1, 2
Affiliations
- Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
- Department of Mathematics, University of Chicago, 5734 University Avenue, Chicago, Illinois 60637, U.S.A.
Abstract
We prove that there exists a real or complex central simple associative algebra M with minimal one-sided ideals such that, for every non-Jordan associative polynomial p, a Jordan-algebra norm can be given on M in such a way that the action of p on M becomes discontinuous.
Bibliography
- R. Arens and M. Goldberg, Quadrative seminorms and Jordan structures on algebras, Linear Algebra Appl. 181 (1993), 269-278.
- R. Arens, M. Goldberg and W. A. J. Luxemburg, Multiplicativity factors for seminorms II, J. Math. Anal. Appl. 170 (1992), 401-413.
- M. Cabrera, A. Moreno and A. Rodríguez, Zel'manov's theorem for primitive Jordan-Banach algebras, J. London Math. Soc., to appear.
- M. Cabrera, A. Moreno and A. Rodríguez, On the behaviour of Jordan-algebra norms on associative algebras, Studia Math. 113 (1995), 81-100.
- M. Cabrera and A. Rodríguez, Zel'manov's theorem for normed simple Jordan algebras with a unit, Bull. London Math. Soc. 25 (1993), 59-63.
- M. Cabrera and A. Rodríguez, Non-degenerately ultraprime Jordan-Banach algebras: a zel'manovian treatment, Proc. London Math. Soc. 69 (1994), 576-604.
- A. Fernández, E. García and A. Rodríguez, A Zel'manov prime theorem for JB*-algebras, J. London Math. Soc. 46 (1992), 319-335.
- N. Jacobson, Lectures in Abstract Algebra. II. Linear Algebra, Grad. Texts in Math. 31, Springer, New York, 1953.
- N. Jacobson, Structure and Representations of Jordan Algebras, Amer. Math. Soc. Colloq. Publ. 39, Providence, R.I., 1968.
- J. M. Osborn and M. L. Racine, Jordan rings with nonzero socle, Trans. Amer. Math. Soc. 251 (1979), 375-387.
- J. Pérez, L. Rico, A. Rodríguez and A. R. Villena, Prime Jordan-Banach algebras with nonzero socle, Comm. Algebra 20 (1992), 17-53.
- H.-G. Quebbemann, A representation theorem for algebras with involution, Linear Algebra Appl. 94 (1987), 193-195.
- C. E. Rickart, General Theory of Banach Algebras, Krieger, New York, 1974.
- A. Rodríguez, La continuidad del producto de Jordan implica la del ordinario en el caso completo semiprimo, in: Contribuciones en Probabilidad, Estadí stica Matemática, Enseñanza de la Matemática y Análisis, Secretariado de Publicaciones de la Universidad de Granada, Granada, 1979, 280-288.
- A. Rodríguez, Jordan axioms for C*-algebras, Manuscripta Math. 61 (1988), 297-314.
- A. Rodríguez, Jordan structures in analysis, in: Jordan Algebras, Proc. Conf. Oberwolfach, August 9-15, 1992, W. Kaup, K. McCrimmon and H. Petersson (eds.), de Gruyter, Berlin, 1994, 97-186.
- A. Rodríguez, A. Slin'ko and E. Zel'manov, Extending the norm from Jordan-Banach algebras of hermitian elements to their associative envelopes, Comm. Algebra 22 (1994), 1435-1455.
- E. Zel'manov, On prime Jordan algebras II, Siberian Math. J. 24 (1983), 89-104.