Common properties of bounded linear operators <em>AC</em> and <em>BA</em>: Local spectral theory期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Qingping Zeng Huaijie Zhong

Institution:	1. College of Computer and Information, Fujian Agriculture and Forestry University, Fuzhou 350002, PR China;2. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, PR China

Abstract:	Let X, Y be Banach spaces, A:X→Y $A : X \to Y$ and B,C:Y→X $B, C : Y \to X$ be bounded linear operators satisfying operator equation ABA=ACA $A B A = A C A$ . In this paper, we show that AC and BA share the local spectral properties such as Bishop's property (β), subscalarity and Dunford's property (C). Also, the quasi-nilpotent part and the analytic core for AC and BA are studied.

Keywords:	Jacobson's lemma Operator equation Common property Local spectral theory
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