For = ℝ or ℂ we exhibit a Jordan-algebra norm ⎮·⎮ on the simple associative algebra with the property that Jordan polynomials over are precisely those associative polynomials over which act ⎮·⎮-continuously on . This analytic determination of Jordan polynomials improves the one recently obtained in [5].
@article{bwmeta1.element.bwnjournal-article-smv122i1p67bwm, author = {A. Moreno Galindo}, title = {Distinguishing Jordan polynomials by means of a single Jordan-algebra norm}, journal = {Studia Mathematica}, volume = {122}, year = {1997}, pages = {67-73}, zbl = {0887.46031}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv122i1p67bwm} }
Moreno Galindo, A. Distinguishing Jordan polynomials by means of a single Jordan-algebra norm. Studia Mathematica, Tome 122 (1997) pp. 67-73. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv122i1p67bwm/
[00000] [1] R. Arens and M. Goldberg, Quadrative seminorms and Jordan structures on algebras, Linear Algebra Appl. 181 (1993), 269-278. | Zbl 0827.46047
[00001] [2] R. Arens, M. Goldberg and W. A. J. Luxemburg, Multiplicativity factors for seminorms II, J. Math. Anal. Appl. 170 (1992), 401-413. | Zbl 0796.46034
[00002] [3] M. Cabrera, A. Moreno and A. Rodríguez, On the behaviour of Jordan-algebra norms on associative algebras, Studia Math. 113 (1995), 81-100. | Zbl 0826.17038
[00003] [4] M. Cabrera, A. Moreno and A. Rodríguez, Zel'manov's theorem for primitive Jordan-Banach algebras, J. London Math. Soc., to appear. | Zbl 0922.17019
[00004] [5] M. Cabrera, A. Moreno, A. Rodríguez and E. Zel'manov, Jordan polynomials can be analytically recognized, Studia Math. 117 (1996), 137-147. | Zbl 0852.17033
[00005] [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.
[00006] [7] M. Cabrera and A. Rodríguez, Nondegenerately ultraprime Jordan-Banach algebras: a zel'manovian treatment, Proc. London Math. Soc. 69 (1994), 576-604. | Zbl 0809.46044
[00007] [8] A. Fernández, E. García and A. Rodríguez, A Zel'manov prime theorem for JB*-algebras, J. London Math. Soc. 46 (1992), 319-335. | Zbl 0723.17025
[00008] [9] A. Moreno and A. Rodríguez, Algebra norms on tensor products of algebras and the norm extension problem, preprint, Universidad de Granada, 1995.
[00009] [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.
[00010] [11] A. Rodríguez, Jordan axioms for C*-algebras, Manuscripta Math. 61 (1988), 297-314.
[00011] [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. | Zbl 0818.17036
[00012] [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. | Zbl 0806.17033
[00013] [14] S. Shirali, On the Jordan structure of complex Banach *-algebras, Pacific J. Math. 27 (1968), 397-404. | Zbl 0182.17802
[00014] [15] E. Zel'manov, On prime Jordan algebras II, Siberian Math. J. 24 (1983), 89-104.