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Maps preserving the local spectrum of Jordan product of matrices
Journal article   Open access  Peer reviewed

Maps preserving the local spectrum of Jordan product of matrices

Abdellatif Bourhim and Mohamed Mabrouk
Linear algebra and its applications, Vol.484, pp.379-395
01/11/2015
DOI: https://doi.org/10.1016/j.laa.2015.06.034

Abstract

Jordan product Local spectrum Nonlinear preservers The single-valued extension property
Let Mn(C) be the algebra of all n×n complex matrices, and fix a nonzero vector x0∈Cn. We show that a map φ from Mn(C) into itself satisfiesσφ(T)φ(S)+φ(S)φ(T)(x0) = σTS+ST(x0), (T, S∈Mn(C)), if and only if there exists an invertible matrix A∈Mn(C) such that Ax0=x0 and φ(T)=±ATA−1 for all T∈Mn(C).
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https://doi.org/10.1016/j.laa.2015.06.034View
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