Peripheral Local Spectrum Preservers of Jordan Products of Operators

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Abstract

We completely describe surjective maps preserving the peripheral local spectrum of Jordan product of operators. Let \(x_0 \in X\) and \(y_0 \in Y \) be two nonzero vectors. We show that a map \(\varphi \) from B(X) onto B(Y) satisfies
$$\begin{aligned} \gamma _{ST+ TS}(x_0)=\gamma _{\varphi (S)\varphi (T)+ \varphi (T)\varphi (S)}(y_0), \quad (T,S\in B(X)), \end{aligned}$$
if and only if there exists a bijective bounded linear map from X into Y such that\( A(x_0)=y_0\) and either \(\varphi (T)=-ATA^{-1}\) for all \(T \in B(X) \) or \(\varphi (T)=ATA^{-1}\) for all \(T \in B(X)\).

Keywords

Jordan product Peripheral spectrum Nonlinear preserver maps 

Mathematics Subject Classification

Primary 47B49 Secondary 47A10 47A11 
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Copyright information

© Iranian Mathematical Society 2018

Authors and Affiliations

  1. 1.Department of mathematics, Faculty of sciencesUniversity of ZanjanZanjanIran

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