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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Spectrum preserving linear mappings for scattered Jordan-Banach algebras


Author: Abdelaziz Maouche
Journal: Proc. Amer. Math. Soc. 127 (1999), 3187-3190
MSC (1991): Primary 46H70; Secondary 17A15
DOI: https://doi.org/10.1090/S0002-9939-99-04933-3
Published electronically: May 19, 1999
MathSciNet review: 1610749
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Abstract: Given two semisimple complex Jordan-Banach algebras with identity $A$ and $B$, we say that $T$ is a spectrum preserving linear mapping from $A$ to $B$ if $T$ is surjective and we have $\operatorname{Sp}(Tx)=\operatorname{Sp}(x)$, for all $x\in A$. We prove that if $B$ is a scattered Jordan-Banach algebra, then $T$ is a Jordan isomorphism.


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Additional Information

Abdelaziz Maouche
Affiliation: Département de Mathématiques et de Statistique, Université Laval, Québec, Canada G1K 7P4

DOI: https://doi.org/10.1090/S0002-9939-99-04933-3
Keywords: Spectrum linear preserving mapping, socle, annihilator, scattered Jordan-Banach algebra, Jordan isomorphism
Received by editor(s): November 7, 1996
Received by editor(s) in revised form: January 9, 1998
Published electronically: May 19, 1999
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1999 American Mathematical Society