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 50 条

[1] Continuous maps preserving local spectra of matrices
Costara, Constantin
LINEAR ALGEBRA AND ITS APPLICATIONS, 2016, 492 : 1 - 8
[2] Surjective linear maps preserving local spectra
Bourhim, Abdellatif
LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 432 (01) : 383 - 393
[3] Maps preserving the local spectrum of Jordan product of matrices
Bourhim, Abdellatif
Mabrouk, Mohamed
LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 484 : 379 - 395
[4] Surjective maps on matrices preserving the local spectral radius distance
Costara, Constantin
LINEAR & MULTILINEAR ALGEBRA, 2014, 62 (07) : 988 - 994
[5] Maps preserving the local spectrum of quadratic products of matrices
Zine El Abidine Abdelali
Abdellatif Bourhim
Acta Scientiarum Mathematicarum, 2018, 84 (1-2): : 49 - 64
[6] Maps preserving the local spectrum of quadratic products of matrices
Abdelali, Zine El Abidine
Bourhim, Abdellatif
ACTA SCIENTIARUM MATHEMATICARUM, 2018, 84 (1-2): : 49 - 64
[7] Linear Maps Preserving Matrices of Local Spectral Radius Zero at a Fixed Vector
Bourhim, Abdellatif
Costara, Constantin
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2019, 71 (04): : 749 - 771
[8] Holomorphic maps preserving parts of the local spectrum
Costara, Constantin
ARCHIV DER MATHEMATIK, 2015, 105 (02) : 153 - 162
[9] Maps on matrices compressing the local spectrum in the spectrum
Benbouziane, Hassane
El Kettani, Mustapha Ech-Cherif
LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 475 : 176 - 185
[10] Additive maps preserving matrices of inner local spectral radius zero at some fixed vector
Costara, Constantin
COMPLEX ANALYSIS AND SPECTRAL THEORY, 2020, 743 : 1 - 9

← 1 2 3 4 5 →