Additive maps onto matrix spaces compressing the spectrum

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:437

Article

Costara, Constantin¹ 

[1] Ovidius Univ, Fac Math & Informat, Mamaia Boul 124, Constanta 900527, Romania

关键词: Preserver;    Spectrum;    Additive;    Banach algebras;    Matrix spaces;   

DOI  :  10.1016/j.jmaa.2016.01.048

来源: Elsevier

【 摘 要 】

We prove that given a unital C*-algebra A and an additive and surjective map T : A -> M-n, such that the spectrum of T(x) is a subset of the spectrum of x for each x is an element of A, then T is either an algebra morphism, or an algebra anti-morphism. We arrive at the same conclusion for an arbitrary unital, complex Banach algebra A, by imposing an extra surjectivity condition on the map T. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free