Geodesic
Linear maps on $M_n(\mathbb C)$ preserving the local spectral radius
Abdellatif Bourhim1 ; Vivien G. Miller2
1Département de mathématiques et de statistique Université Laval Québec, Canada G1K 7P4
2Department 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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