Maps on matrices preserving local spectra

被引：13
|
作者：
Bendaoud, M. [1 ]
Douimi, M. [1 ]
Sarih, M. [2 ]
机构：
[1] Univ Moulay Ismail, Ecole Natl Super Arts & Metiers, Dept Math & Informat, Beni Mhamed, Meknes, Morocco
[2] Univ Moulay Ismail, Fac Sci, Dept Math, Zitoune, Meknes, Morocco
来源：
LINEAR & MULTILINEAR ALGEBRA | 2013年 / 61卷 / 07期
关键词：
local spectrum; local spectral radius; preserver problems; LINEAR-MAPS;
D O I：
10.1080/03081087.2012.716429
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For a square matrix T and a nonzero vector eC(n), let sigma(T)(x) be the local spectrum of T at e. Characterization is obtained for surjective maps phi on M-n(C) satisfying sigma(phi(T)-phi(S))(e)sigma(T-S)(e) for all matrices T and S. The same description is obtained by supposing that sigma(T-S)(e)sigma(phi(T)-phi(S))(e) for all matrices T and S, without the surjectivity assumption on phi. Continuous maps from M-n(C) onto itself that preserve the local spectral radius distance at a nonzero fixed vector are also characterized.
引用
收藏
页码：871 / 880
页数：10
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