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

[21] Idempotence preserving maps on spaces of triangular matrices
Sheng Y.
Zheng B.
Zhang X.
Journal of Applied Mathematics and Computing, 2007, 25 (1-2) : 17 - 33
[22] Maps preserving invertibility of matrices over semirings
Pshenitsyna, O. A.
RUSSIAN MATHEMATICAL SURVEYS, 2009, 64 (01) : 162 - 164
[23] Continuous adjacency preserving maps on real matrices
Rodman, L
Semrl, P
Sourour, AR
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2005, 48 (02): : 267 - 274
[24] On maps preserving square-zero matrices
Chebotar, MA
Ke, WF
Lee, PH
JOURNAL OF ALGEBRA, 2005, 289 (02) : 421 - 445
[25] SIMILARITY PRESERVING LINEAR-MAPS ON MATRICES
HIAI, F
LINEAR ALGEBRA AND ITS APPLICATIONS, 1987, 97 : 127 - 139
[26] Maps preserving the spectrum of polynomial products of matrices
El Abidine Abdelali, Zine
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 480 (02)
[27] Multiplicatively spectrum preserving maps on rectangular matrices
Abdelali, Zine El Abidine
Aharmim, Bouchra
LINEAR & MULTILINEAR ALGEBRA, 2021, 69 (16): : 3099 - 3111
[28] Maps preserving matrices of extremal scrambling index
Guterman, A. E.
Maksaev, A. M.
SPECIAL MATRICES, 2018, 6 (01): : 166 - 179
[29] Linear maps preserving permutation and stochastic matrices
Li, CK
Tam, BS
Tsing, NK
LINEAR ALGEBRA AND ITS APPLICATIONS, 2002, 341 : 5 - 22
[30] 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 →