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

页码：871 / 880

页数：10

共 15 条

[1]

Aiena P., 2004, Fredholm and Local Spectral Theory, with Application to Multipliers

[2]

Aupetit B., 1991, A Primer on Spectral Theory

[3]

Bendaoud M, 2011, MATH BOHEM, V136, P81

[4] Additive local spectrum compressors [J].