Jordan polynomials can be analytically recognized

M. Cabrera Garcia; A. Moreno Galindo; A. Rodríguez Palacios; E. Zel'manov

Studia Mathematica (1996)

  • Volume: 117, Issue: 2, page 137-147
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Cabrera Garcia, M., et al. "Jordan polynomials can be analytically recognized." Studia Mathematica 117.2 (1996): 137-147. <http://eudml.org/doc/216248>.

@article{CabreraGarcia1996,
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.},
author = {Cabrera Garcia, M., Moreno Galindo, A., Rodríguez Palacios, A., Zel'manov, E.},
journal = {Studia Mathematica},
keywords = {central simple associative algebra; minimal one-sided ideals; non-Jordan associative polynomial; Jordan algebra norm},
language = {eng},
number = {2},
pages = {137-147},
title = {Jordan polynomials can be analytically recognized},
url = {http://eudml.org/doc/216248},
volume = {117},
year = {1996},
}

TY - JOUR
AU - Cabrera Garcia, M.
AU - Moreno Galindo, A.
AU - Rodríguez Palacios, A.
AU - Zel'manov, E.
TI - Jordan polynomials can be analytically recognized
JO - Studia Mathematica
PY - 1996
VL - 117
IS - 2
SP - 137
EP - 147
AB - 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.
LA - eng
KW - central simple associative algebra; minimal one-sided ideals; non-Jordan associative polynomial; Jordan algebra norm
UR - http://eudml.org/doc/216248
ER -

References

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  2. [2] R. Arens, M. Goldberg and W. A. J. Luxemburg, Multiplicativity factors for seminorms II, J. Math. Anal. Appl. 170 (1992), 401-413. Zbl0796.46034
  3. [3] M. Cabrera, A. Moreno and A. Rodríguez, Zel'manov's theorem for primitive Jordan-Banach algebras, J. London Math. Soc., to appear. Zbl0922.17019
  4. [4] M. Cabrera, A. Moreno and A. Rodríguez, On the behaviour of Jordan-algebra norms on associative algebras, Studia Math. 113 (1995), 81-100. Zbl0826.17038
  5. [5] 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. 
  6. [6] M. Cabrera and A. Rodríguez, Non-degenerately ultraprime Jordan-Banach algebras: a zel'manovian treatment, Proc. London Math. Soc. 69 (1994), 576-604. Zbl0809.46044
  7. [7] A. Fernández, E. García and A. Rodríguez, A Zel'manov prime theorem for JB*-algebras, J. London Math. Soc. 46 (1992), 319-335. Zbl0723.17025
  8. [8] N. Jacobson, Lectures in Abstract Algebra. II. Linear Algebra, Grad. Texts in Math. 31, Springer, New York, 1953. 
  9. [9] N. Jacobson, Structure and Representations of Jordan Algebras, Amer. Math. Soc. Colloq. Publ. 39, Providence, R.I., 1968. 
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  11. [11] J. Pérez, L. Rico, A. Rodríguez and A. R. Villena, Prime Jordan-Banach algebras with nonzero socle, Comm. Algebra 20 (1992), 17-53. Zbl0742.17028
  12. [12] H.-G. Quebbemann, A representation theorem for algebras with involution, Linear Algebra Appl. 94 (1987), 193-195. Zbl0621.16013
  13. [13] C. E. Rickart, General Theory of Banach Algebras, Krieger, New York, 1974. Zbl0275.46045
  14. [14] 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. 
  15. [15] A. Rodríguez, Jordan axioms for C*-algebras, Manuscripta Math. 61 (1988), 297-314. 
  16. [16] 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. Zbl0818.17036
  17. [17] 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. Zbl0806.17033
  18. [18] E. Zel'manov, On prime Jordan algebras II, Siberian Math. J. 24 (1983), 89-104. 

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