有界线性算子的Weyl定理的判定  

The judgement of Weyl’s theorem for bounded linear operators

作　　者：王静 曹小红[1] WANG Jing;CAO Xiaohong(School of Mathematics and Information Science,Shaanxi Normal University,Xi’an 710062,China)

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《浙江大学学报（理学版）》2020年第5期541-547,553,共8页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(11471200).

摘　　要：令H为无限维复可分的Hilbert空间,B(H)为H上有界线性算子的全体,若σ(T)\σw(T)⊆π00(T)或σw(T)=σb(T),称算子T∈B(H)满足Browder定理;若σ(T)\σw(T)=π00(T),称T满足Weyl定理;其中σ(T),σw(T),σb(T)分别表示算子T的谱集、Weyl谱、Browder谱,π00(T)={λ∈isoσ(T):0<dimN(T-λI)<∞}。研究了算子及其函数的Weyl定理,给出了算子及其函数满足Weyl定理的判定方法,并讨论了相应谱集的谱映射定理。Let H be an infinite dimensional separable complex Hilbert space and B(H)be the algebra of all bounded linear operators on H.We call T∈B(H)satisfies the Browder’s theorem ifσ(T)\σw(T)?π00(T)orσw(T)=σb(T);we call T satisfies the Weyl’s theorem ifσ(T)\σw(T)=π00(T),whereσ(T),σw(T),σb(T)denote the spectrum,Weyl spectrum,and Browder spectrum of T,respectively,π00(T)={λ∈isoσ(T):0<dim N(T-λI)<∞}.In this note,we explore the Weyl’s theorem for operator and its functional,and get a new judgement for the Weyl’s theorem.In addition,we consider the spectrum mapping theorem for some new spectrum.

关 键 词：BROWDER定理 WEYL定理 谱 

分 类 号：O177.2[理学—数学]