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Linear Maps Preserving Matrices of Local Spectral Radius Zero at a Fixed Vector

Part of: Special classes of linear operators General theory of linear operators

Published online by Cambridge University Press:  07 January 2019

Abdellatif Bourhim  and
Constantin Costara
Abdellatif Bourhim
Affiliation:
Department of Mathematics, Syracuse University, Syracuse, NY 13244, USA Email: abourhim@syr.edu
Constantin Costara
Affiliation:
Faculty of Mathematics and Informatics, Ovidius University of Constanţa, Mamaia Boul. 124, 900527, Constanţa, Romania Email: cdcostara@univ-ovidius.ro
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Abstract

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In this paper, we characterize linear maps on matrix spaces that preserve matrices of local spectral radius zero at some fixed nonzero vector.

Keywords

linear preserverlocal spectrumlocal spectral radiusmatrix

MSC classification

Primary: 47B49: Transformers, preservers (operators on spaces of operators)
Secondary: 47A10: Spectrum, resolvent 47A11: Local spectral properties
Type
Article
Information
Canadian Journal of Mathematics , Volume 71 , Issue 4 , August 2019 , pp. 749 - 771
Copyright
© Canadian Mathematical Society 2018 

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