Linear maps on Mₙ(ℂ) preserving the local spectral radius

Abdellatif Bourhim, and Vivien G. Miller. "Linear maps on Mₙ(ℂ) preserving the local spectral radius." Studia Mathematica 188.1 (2008): 67-75. <http://eudml.org/doc/284753>.

@article{AbdellatifBourhim2008,
abstract = {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).},
author = {Abdellatif Bourhim, Vivien G. Miller},
journal = {Studia Mathematica},
keywords = {linear preservers; spectrally bounded map; local spectrum; local spectral radius; single-valued extension property},
language = {eng},
number = {1},
pages = {67-75},
title = {Linear maps on Mₙ(ℂ) preserving the local spectral radius},
url = {http://eudml.org/doc/284753},
volume = {188},
year = {2008},
}

TY - JOUR
AU - Abdellatif Bourhim
AU - Vivien G. Miller
TI - Linear maps on Mₙ(ℂ) preserving the local spectral radius
JO - Studia Mathematica
PY - 2008
VL - 188
IS - 1
SP - 67
EP - 75
AB - 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).
LA - eng
KW - linear preservers; spectrally bounded map; local spectrum; local spectral radius; single-valued extension property
UR - http://eudml.org/doc/284753
ER -