Preservers of pseudo spectral radius of operator products

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• 作者：M. Bendaoud^a ; ^{m.bendaoud@ensam-umi.ac.ma" class="auth_mail" title="E-mail the corresponding author} ; A. Benyouness^b ; ^{benyouness@fs-umi.ac.ma" class="auth_mail" title="E-mail the corresponding author} ; M. Sarih^b ; ^{sarih@fs-umi.ac.ma" class="auth_mail" title="E-mail the corresponding author}
• 关键词：47B49 ; 47A10 ; 47A25
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：489
• 期：Complete
• 页码：186-198
• 全文大小：308 K

文摘

Let H$\mathcal{H}$ be an infinite-dimensional complex Hilbert space and let L(H)$\mathcal{L}(\mathcal{H})$ be the algebra of all bounded linear operators on H$\mathcal{H}$. For ε>0$\epsilon >0$ and T∈L(H)$T\in \mathcal{L}(\mathcal{H})$, let r_ε(T)$r_{\epsilon }(T)$ denote the ε-pseudo spectral radius of T. We characterize surjective maps ϕ   on L(H)$\mathcal{L}(\mathcal{H})$ which satisfy for all T,S∈L(H)$T,S\in \mathcal{L}(\mathcal{H})$. We also obtain analogous result for the finite-dimensional case, without the surjectivity assumption on ϕ.