Nonlinear maps preserving the minimum and surjectivity moduli

被引：12

作者：

Bourhim, A. ^{[1
]}

Mashreghi, J. ^{[2
]}

Stepanyan, A. ^{[2
]}

机构：

[1] Syracuse Univ, Dept Math, Syracuse, NY 13244 USA

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

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2014年 / 463卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Preservers; Minimum moduli; Surjectivity moduli; PERIPHERALLY-MULTIPLICATIVE SURJECTIONS; ALGEBRA ISOMORPHISMS; JORDAN ISOMORPHISMS; MAPPINGS; MATRICES; SPACE; INVERTIBILITY; SPECTRA;

D O I：

10.1016/j.laa.2014.09.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let X and Y be infinite-dimensional complex Banach spaces, and let B(X) (resp. B(Y)) denote the algebra of all bounded linear operators on X (resp. on Y). We describe maps phi from B(X) onto B(Y) satisfying c(phi(S) +/- phi(T)) = c(S +/- T) for all S,T epsilon B(X), where c(.) stands either for the minimum modulus, or the surjectivity modulus, or the maximum modulus. We also obtain analog results for the finite-dimensional case. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：171 / 189

页数：19

共 38 条

[1] A hereditarily indecomposable L∞-space that solves the scalar-plus-compact problem [J].