Geodesic
Linear maps on $M_n(\mathbb C)$ preserving the local spectral radius
Abdellatif Bourhim 1   ; Vivien G. Miller 2
1 Département de mathématiques et de statistique Université Laval Québec, Canada G1K 7P4
2 Department of Mathematics and Statistics Mississippi State University Mississippi State, MS 39762, U.S.A.
Studia Mathematica, Tome 188 (2008) no. 1, pp. 67-75 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $T\in M_n(\mathbb C)$.
DOI : 10.4064/sm188-1-4
Keywords: nonzero vector mathbb linear map mit phi mathbb mathbb preserves local spectral radius only there alpha mathbb modulus invertible matrix mathbb mit phi alpha ata mathbb

Abdellatif Bourhim  1   ; Vivien G. Miller  2

1 Département de mathématiques et de statistique Université Laval Québec, Canada G1K 7P4
2 Department of Mathematics and Statistics Mississippi State University Mississippi State, MS 39762, U.S.A. 
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Abdellatif Bourhim; Vivien G. Miller. Linear maps on $M_n(\mathbb C)$ preserving the local spectral radius. Studia Mathematica, Tome 188 (2008) no. 1, pp. 67-75. doi: 10.4064/sm188-1-4

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