Linear maps on Mₙ(ℂ) preserving the local spectral radius
Abdellatif Bourhim ; Vivien G. Miller
Studia Mathematica, Tome 187 (2008), p. 67-75 / Harvested from The Polish Digital Mathematics Library
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Let x₀ be a nonzero vector in ℂⁿ. We show that a linear map Φ: Mₙ(ℂ) → Mₙ(ℂ) preserves the local spectral radius at x₀ if and only if there is α ∈ ℂ of modulus one and an invertible matrix A ∈ Mₙ(ℂ) such that Ax₀ = x₀ and Φ(T)=αATA-1 for all T ∈ Mₙ(ℂ).

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:284753 
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     title = {Linear maps on Mn(C) preserving the local spectral radius},
     journal = {Studia Mathematica},
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     year = {2008},
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Abdellatif Bourhim; Vivien G. Miller. Linear maps on Mₙ(ℂ) preserving the local spectral radius. Studia Mathematica, Tome 187 (2008) pp. 67-75. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm188-1-4/