Spectral preservers and approximate spectral preservers on operator algebras

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• 作者：J. Alaminos ^{alaminos@ugr.es" class="auth_mail" title="E-mail the corresponding author} ; J. Extremera ^{jlizana@ugr.es" class="auth_mail" title="E-mail the corresponding author} ; A.R. Villena ; ^{avillena@ugr.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 47A10 ; 47B49 ; secondary ; 15A86 ; 47L10
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：1 May 2016
• 年：2016
• 卷：496
• 期：Complete
• 页码：36-70
• 全文大小：602 K

文摘

Let A$\mathcal{A}$ and B$\mathcal{B}$ be unital primitive Banach algebras with minimal idempotents. We prove that every surjective spectral isometry from A$\mathcal{A}$ onto B$\mathcal{B}$ is of the form λ  Ψ where a65f588e4" title="Click to view the MathML source">λ∈C$\lambda \in \mathbb{C}$ with |λ|=1$|\lambda |=1$ and Ψ is either an isomorphism or an anti-isomorphism from A$\mathcal{A}$ onto B$\mathcal{B}$. As an application we show that, for all Banach spaces X and Y  , the spectral nearisometries and the approximate spectrum-preserving maps from L(X)$\mathcal{L}(X)$ onto L(Y)$\mathcal{L}(Y)$ are perturbations of actual spectral isometries and spectrum-preserving maps, respectively.