Maps preserving the local spectrum of quadratic products of matrices

Abdelali, Zine El Abidine and Bourhim, Abdellatif: Maps preserving the local spectrum of quadratic products of matrices. Acta scientiarum mathematicarum, (84) 1-2. pp. 49-64. (2018)

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Abstract

Let Mn(C) denote the algebra of all n × n complex matrices, and fix a nonzero vector x0 in C n . For any matrix T ∈ Mn(C), let σT (x0) denote the local spectrum of T at x0. Given three scalars µ, ν and ξ simultaneously nonzero, we study maps ϕ on Mn(C) satisfying σµST S+νT S+ξST (x0) = σµϕ(S)ϕ(T )ϕ(S)+νϕ(T )ϕ(S)+ξϕ(S)ϕ(T )(x0) for all S, T ∈ Mn(C). Our main result extends and unifies the main results of several papers on maps on Mn(C) preserving the local spectrum of different products.

Item Type: Article
Journal or Publication Title: Acta scientiarum mathematicarum
Date: 2018
Volume: 84
Number: 1-2
Page Range: pp. 49-64
ISSN: 0001-6969
Uncontrolled Keywords: Mátrixelmélet, Leképezés
Additional Information: Bibliogr.: p. 62-64. ; Összefoglalás angol nyelven
Official URL: http://www.acta.hu
Date Deposited: 2018. Nov. 10. 09:31
Last Modified: 2019. Sep. 09. 13:44
URI: http://acta.bibl.u-szeged.hu/id/eprint/55803

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