Characterizing isomorphisms in terms of completely preserving invertibility or spectrum

被引：35

作者：

Hou, Jinchuan ^{[1
]}

Huang, Li ^{[2
]}

机构：

[1] Taiyuan Univ Technol, Dept Math, Taiyuan 030024, Peoples R China

[2] Taiyuan Univ Sci & Technol, Dept Math, Taiyuan 0300024, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2009年 / 359卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Standard operator algebras; Isomorphisms; Invertibility; Spectra; Completely preserver problems; STANDARD OPERATOR-ALGEBRAS; LINEAR-MAPS; ELEMENTARY OPERATORS; BANACH-ALGEBRAS; ADDITIVE MAPS;

D O I：

10.1016/j.jmaa.2009.05.041

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let A and B tie standard operator algebras on complex Banach spaces X and Y, respectively. In this paper, we characterize the surjective maps completely preserving the invertibility in both directions and the surjective maps completely preserving the spectrum from A to B. We show that a surjective map from A to B is a ring isomorphism if and only if it is unital and completely preserves the invertibility of operators in both directions; is an isomorphism if and only if it completely preserves the spectrum of operators. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：81 / 87

页数：7