On maps preserving operators of local spectral radius zero

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• 作者：M. Elhodaibi^a ; ^{hodaibi2001@yahoo.fr" class="auth_mail" title="E-mail the corresponding author} ; A. Jaatit^b ; ^{a.jaatit@hotmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 47B49 ; secondary ; 47B48 ; 47A10 ; 47A11
• 刊名：Linear Algebra and its Applications
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：512
• 期：Complete
• 页码：191-201
• 全文大小：267 K

文摘

Let e7e0dc6f9c83" title="Click to view the MathML source">L(X)$\mathcal{L}(X)$ be the algebra of all bounded linear operators on a complex Banach space X. We describe surjective linear maps ϕ   on e7e0dc6f9c83" title="Click to view the MathML source">L(X)$\mathcal{L}(X)$ that satisfy for every e80a5bf6f8136a953e91f47a14f0" title="Click to view the MathML source">x∈X$x\in X$ and bd335f84309015" title="Click to view the MathML source">T∈L(X)$T\in \mathcal{L}(X)$. We also describe surjective linear maps ϕ   on e7e0dc6f9c83" title="Click to view the MathML source">L(X)$\mathcal{L}(X)$ that satisfy for every e80a5bf6f8136a953e91f47a14f0" title="Click to view the MathML source">x∈X$x\in X$ and bd335f84309015" title="Click to view the MathML source">T∈L(X)$T\in \mathcal{L}(X)$. Furthermore, we characterize maps ϕ   (not necessarily linear nor surjective) on e7e0dc6f9c83" title="Click to view the MathML source">L(X)$\mathcal{L}(X)$ which satisfy for every e80a5bf6f8136a953e91f47a14f0" title="Click to view the MathML source">x∈X$x\in X$ and e88db17bf407ac2ea" title="Click to view the MathML source">T,S∈L(X)$T,S\in \mathcal{L}(X)$.