陕西师范大学学报（自然科学版）2017，Vol.45Issue(5)：6-11,6.DOI:10.15983/j.cnki.jsnu.2017.05.152
算子函数演算的Wey1定理
Weyl's theorem for the functions of operators
摘要
Abstract
Let H be an infinite dimensional separable complex Hilbert space and B(H) the algebra of all bounded linear operators on H.An operator T∈ B(H) is said to satisfy Weyl's theorem if σ(T) \σw (T) =π00 (T),where σ(T) and σw (T) denote the spectrum and Weyl spectrum of operator T respectively,and π00 (T) denotes the set of all isolated eigenvalues of finite multiplicity.In this note,it is given that the definition of the Weyl-Kato decomposition of a bounded linear operator on Hilbert space.Using the new spectrum defined by the definition of the Weyl-Kato decomposition,it is established that sufficient and necessary conditions for Weyl's theorem for the functions of operators.关键词
Weyl-Kato分解/Weyl定理/紧摄动Key words
Weyl-Kato decomposition/Weyl's theorem/compact perturbations分类
数理科学引用本文复制引用
董炯,曹小红..算子函数演算的Wey1定理[J].陕西师范大学学报（自然科学版）,2017,45(5):6-11,6.基金项目
国家自然科学基金(11371012,11471200,11571213) （11371012,11471200,11571213）
中央高校基本科研业务费专项资金(GK201601004) （GK201601004）
