Maps on matrices preserving local spectra

For a square matrix T and a nonzero vector e ∈ ℂ n , let σ T (x) be the local spectrum of T at e. Characterization is obtained for surjective maps φ on ℳ n (ℂ) satisfying σ φ(T)−φ(S) (e) ⊆ σ T−S (e) for all matrices T and S. The same description is obtained by supposing that σ T−S (e) ⊆ σ φ(T)−φ(S)...

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Bibliographic Details
Published inLinear & multilinear algebra Vol. 61; no. 7; pp. 871 - 880
Main Authors Bendaoud, M., Douimi, M., Sarih, M.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis Group 01.07.2013
Taylor & Francis Ltd
Subjects
Algebra
local spectral radius
local spectrum
Mathematical analysis
Mathematical problems
Power plants
preserver problems
Preserves
Preserving
Primary: 47B49
Secondary: 47A10
Spectra
Vectors (mathematics)
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Summary:For a square matrix T and a nonzero vector e ∈ ℂ n , let σ T (x) be the local spectrum of T at e. Characterization is obtained for surjective maps φ on ℳ n (ℂ) satisfying σ φ(T)−φ(S) (e) ⊆ σ T−S (e) for all matrices T and S. The same description is obtained by supposing that σ T−S (e) ⊆ σ φ(T)−φ(S) (e) for all matrices T and S, without the surjectivity assumption on φ. Continuous maps from ℳ n (ℂ) onto itself that preserve the local spectral radius distance at a nonzero fixed vector are also characterized.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2012.716429