Characterizations of automorphisms of operator algebras on Banach spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:430

Article

Huang, Lizhong^1,2  Chen, Lin^1,3  Lu, Fangyan¹ 

[1] Soochow Univ, Dept Math, Suzhou 215006, Peoples R China

[2] Shanxi Datong Univ, Dept Math, Datong 037009, Peoples R China

[3] Anshun Univ, Dept Math & Phys, Anshun 561000, Peoples R China

关键词: Automorphisms;    Projection constant;    Projections;   

DOI  :  10.1016/j.jmaa.2015.04.086

来源: Elsevier

【 摘 要 】

Let X be a complex Banach space of dimension greater than one, and denote by B(X) the algebra of all the bounded linear operators on X. It is shown that if phi: B(X) -> B(X) is a multiplicative map (not assumed linear) and if phi is sufficiently close to a linear automorphism of B(X) in some uniform sense, then it is actually an automorphism. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free