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Spectrum preserving linear mappings for scattered Jordan-Banach algebras
Authors:Abdelaziz Maouche
Institution:Département de Mathématiques et de Statistique, Université Laval, Québec, Canada G1K 7P4
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.

Keywords:Spectrum linear preserving mapping  socle  annihilator  scattered Jordan-Banach algebra  Jordan isomorphism
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