有界线性算子的Weyl型定理及亚循环性  

Weyl type theorem and hypercyclic property 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 710119 ,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710119

出　　处：《中国科学技术大学学报》2020年第4期396-401,共6页JUSTC

基　　金：国家自然科学基金(11471200)资助.

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.称算子T∈B(H)满足Browder定理,若σ(T)\σ_(w)(T)■π_(00)(T)或σ_(w)(T)=σ_(b)(T);若σ(T)\σ_(w)(T)=π_(00)(T),称T满足Weyl定理,其中σ(T),σ_(w)(T),σ_(b)(T)分别表示算子T的谱集、Weyl谱、Browder谱,π_(00)(T)={λ∈isoσ(T):0<dim N(T-λI)<∞}.通过定义新的谱集,研究了当T为亚循环算子时算子及算子函数满足Weyl型定理的充要条件,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.T∈B(H)satisfies Browder’s theorem ifσ(T)\σ_(w)(T)■π_(00)(T)orσ_(w)(T)=σ_(b)(T).Ifσ(T)\σ_(w)(T)=π_(00)(T),Weyl’s theorem holds for T,whereσ(T),σ_(w)(T),σ_(b)(T)denote the spectrum set,Weyl spectrum,and Browder spectrum respectively,andπ_(00)(T)={λ∈isoσ(T):0<dim N(T-λI)<∞}.Using the newly defined spectrum,the sufficient and necessary conditions for operator functions satisfying Weyl type theorem were studied if T is a hypercyclic operator.In addition,the spectrum mapping theorem for some new spectrums was discussed.

关 键 词：BROWDER定理 WEYL定理 谱集 亚循环算子 谱映射定理 

分 类 号：O177.2[理学—数学]