Linear maps on $M_n(\mathbb C)$ preserving the local spectral radius

Tom 188 / 2008

Abdellatif Bourhim, Vivien G. Miller Studia Mathematica 188 (2008), 67-75 MSC: Primary 47B49; Secondary 47A10, 47A11. DOI: 10.4064/sm188-1-4

Streszczenie

Let $x_0$ be a nonzero vector in $\mathbb C^n$. We show that a linear map ${\mit\Phi}:M_n(\mathbb C)\to M_n(\mathbb C)$ preserves the local spectral radius at $x_0$ if and only if there is $\alpha\in\mathbb C$ of modulus one and an invertible matrix $A\in M_n(\mathbb C)$ such that $Ax_0=x_0$ and ${\mit\Phi}(T)=\alpha ATA^{-1}$ for all $T\in M_n(\mathbb C)$.

Autorzy

  • Abdellatif BourhimDépartement de mathématiques et de statistique
    Université Laval
    Québec, Canada G1K 7P4
    e-mail
  • Vivien G. MillerDepartment of Mathematics and Statistics
    Mississippi State University
    Mississippi State, MS 39762, U.S.A.
    e-mail

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