Common properties of bounded linear operators AC and BA: Local spectral theory

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:414

Article

Zeng, Qingping^1,2  Zhong, Huaijie² 

[1] Fujian Agr & Forestry Univ, Coll Comp & Informat, Fuzhou 350002, Peoples R China

[2] Fujian Normal Univ, Sch Math & Comp Sci, Fuzhou 350007, Peoples R China

关键词: Jacobson's lemma;    Operator equation;    Common property;    Local spectral theory;   

DOI  :  10.1016/j.jmaa.2014.01.021

来源: Elsevier

【 摘 要 】

Let X, Y be Banach spaces, A : X -> Y and B,C:Y -> X be bounded linear operators satisfying operator equation ABA= ACA. In this paper, we show that AC and BA share the local spectral properties such as Bishop's property (0), subscalarity and Dunford's property (C). Also, the quasi-nilpotent part and the analytic core for AC and BA are studied. (c) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free