Distinguishing Jordan polynomials by means of a single Jordan-algebra norm

A. Moreno Galindo

Studia Mathematica (1997)

  • Volume: 122, Issue: 1, page 67-73
  • ISSN: 0039-3223

Abstract

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For = ℝ or ℂ we exhibit a Jordan-algebra norm ⎮·⎮ on the simple associative algebra M ∞ ( ) with the property that Jordan polynomials over are precisely those associative polynomials over which act ⎮·⎮-continuously on M ∞ ( ) . This analytic determination of Jordan polynomials improves the one recently obtained in [5].

How to cite

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Moreno Galindo, A.. "Distinguishing Jordan polynomials by means of a single Jordan-algebra norm." Studia Mathematica 122.1 (1997): 67-73. <http://eudml.org/doc/216361>.

@article{MorenoGalindo1997,
abstract = {For = ℝ or ℂ we exhibit a Jordan-algebra norm ⎮·⎮ on the simple associative algebra $M_\{∞\}()$ with the property that Jordan polynomials over are precisely those associative polynomials over which act ⎮·⎮-continuously on $M_\{∞\}()$. This analytic determination of Jordan polynomials improves the one recently obtained in [5].},
author = {Moreno Galindo, A.},
journal = {Studia Mathematica},
keywords = {non-Jordan associative polynomials; associative algebras; Jordan-algebra norms; Zelmanov prime theorem; Jordan algebras},
language = {eng},
number = {1},
pages = {67-73},
title = {Distinguishing Jordan polynomials by means of a single Jordan-algebra norm},
url = {http://eudml.org/doc/216361},
volume = {122},
year = {1997},
}

TY - JOUR
AU - Moreno Galindo, A.
TI - Distinguishing Jordan polynomials by means of a single Jordan-algebra norm
JO - Studia Mathematica
PY - 1997
VL - 122
IS - 1
SP - 67
EP - 73
AB - For = ℝ or ℂ we exhibit a Jordan-algebra norm ⎮·⎮ on the simple associative algebra $M_{∞}()$ with the property that Jordan polynomials over are precisely those associative polynomials over which act ⎮·⎮-continuously on $M_{∞}()$. This analytic determination of Jordan polynomials improves the one recently obtained in [5].
LA - eng
KW - non-Jordan associative polynomials; associative algebras; Jordan-algebra norms; Zelmanov prime theorem; Jordan algebras
UR - http://eudml.org/doc/216361
ER -

References

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  1. [1] R. Arens and M. Goldberg, Quadrative seminorms and Jordan structures on algebras, Linear Algebra Appl. 181 (1993), 269-278. Zbl0827.46047
  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, On the behaviour of Jordan-algebra norms on associative algebras, Studia Math. 113 (1995), 81-100. Zbl0826.17038
  4. [4] M. Cabrera, A. Moreno and A. Rodríguez, Zel'manov's theorem for primitive Jordan-Banach algebras, J. London Math. Soc., to appear. Zbl0922.17019
  5. [5] M. Cabrera, A. Moreno, A. Rodríguez and E. Zel'manov, Jordan polynomials can be analytically recognized, Studia Math. 117 (1996), 137-147. Zbl0852.17033
  6. [6] 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. 
  7. [7] M. Cabrera and A. Rodríguez, Nondegenerately ultraprime Jordan-Banach algebras: a zel'manovian treatment, Proc. London Math. Soc. 69 (1994), 576-604. Zbl0809.46044
  8. [8] 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
  9. [9] A. Moreno and A. Rodríguez, Algebra norms on tensor products of algebras and the norm extension problem, preprint, Universidad de Granada, 1995. 
  10. [10] A. Rodríguez, La continuidad del producto de Jordan implica la del ordinario en el caso completo semiprimo, in: Contribuciones en Probabilidad, Estadística Matemática, Enseñanza de la Matemática y Análisis, Secretariado de Publicaciones de la Universidad de Granada, Granada, 1979, 280-288. 
  11. [11] A. Rodríguez, Jordan axioms for C*-algebras, Manuscripta Math. 61 (1988), 297-314. 
  12. [12] A. Rodríguez, Jordan structures in Analysis, in: Jordan Algebras: Proc. Conf. Oberwolfach, August 9-15, 1992, W. Kaup, K. McCrimmon, and H. Petersson (eds.), Walter de Gruyter, Berlin, 1994, 97-186. Zbl0818.17036
  13. [13] 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
  14. [14] S. Shirali, On the Jordan structure of complex Banach *-algebras, Pacific J. Math. 27 (1968), 397-404. Zbl0182.17802
  15. [15] E. Zel'manov, On prime Jordan algebras II, Siberian Math. J. 24 (1983), 89-104. 

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