Spectrum preserving linear mappings for scattered Jordan-Banach algebras
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- by Abdelaziz Maouche PDF
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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.References
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Additional Information
- Abdelaziz Maouche
- Affiliation: Département de Mathématiques et de Statistique, Université Laval, Québec, Canada G1K 7P4
- 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
- © Copyright 1999 American Mathematical Society
- 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
- MathSciNet review: 1610749