PERIPHERAL LOCAL SPECTRUM PRESERVERS AND MAPS INCREASING THE LOCAL SPECTRAL RADIUS

被引：7

作者：

Bourhim, Abdellatif ^{[1
]}

Jari, Tarik ^{[2
]}

Mashreghi, Javad ^{[2
]}

机构：

[1] Syracuse Univ, Dept Math, 215 Carnegie Bldg, Syracuse, NY 13244 USA

[2] Univ Laval, Dept Math & Stat, Quebec City, PQ G1V 0A6, Canada

来源：

OPERATORS AND MATRICES | 2016年 / 10卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Linear preservers; spectrally bounded map; local spectrum; local spectral radius; the single-valued extension property; BOUNDED LINEAR-MAPS; PRODUCTS; MATRICES; OPERATOR;

D O I：

10.7153/oam-10-12

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We address two long standing problems in the context of local spectral radius preservers. First, we completely describe the form of maps preserving the peripheral local spectrum of product or triple product of operators. Second, we establish the automatic continuity of linear maps increasing the local spectral radius of operators at a fixed nonzero vector.

引用

页码：189 / 208

页数：20

共 32 条

[1]

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

[2]

[Anonymous], RENDICONTI IN PRESS

[3]

Aupetit B., 1991, A Primer on Spectral Theory

[4]

Bhatia R, 1999, STUD MATH, V134, P99

[5]

BOURHIM A., GLASGOW MAT IN PRESS

[6]

Bourhim A., LINEAR MULT IN PRESS

[7]

BOURHIM A., 2015, CRM P LECT IN PRESS

[8] Additive maps preserving local spectrum [J].

Bourhim, Abdellatif ;

Ransford, Thomas .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 2006, 55 (03) :377-385

[9] Local Spectral Radius Preservers [J].

Bourhim, Abdellatif ;

Mashreghi, Javad .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 2013, 76 (01) :95-104

[10] Surjective linear maps preserving local spectra [J].

Bourhim, Abdellatif .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 432 (01) :383-393

← 1 2 3 4 →