有界线性算子及其函数的Browder定理的判定  

Judgement of Browder's Theorem for Bounded Linear Operators and Their Functions

作　　者：白珍贵 曹小红 BAI Zhen-gui;CAO Xiao-hong(School of Mathematics and Statistics,Shanxi Normal University,Xi'an 710062,China;Nanyang No.1 Middle School,Nanyang 473000,China)

机构地区：[1]陕西师范大学数学与统计学院,陕西西安710062 [2]南阳市第一中学校,河南南阳473000

出　　处：《数学的实践与认识》2024年第1期172-181,共10页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11471200)。

摘　　要：令H是无限维的Hilbert空间,B(H)是H上有界线性算子的全体构成的集合.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),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<dimN(T-λI)<∞}.借助新的谱集,给出有界线性算子及其函数满足Browder定理的等价条件.Let H be an infinite dimensional Hilbert space and B(H)be the algebra of all bounded linear operators on H.T E B(H)satisfies the Browder's theorem ifσ(T)\σ_(w)(T)■π_(00)(T)orσ_(w)(T)=σ_(b)(T),whereσ(T),σ_(w)(T),σ_(b)(T)denote the spectrum,Weyl spectrum,Browder spectrum,andπ_(00)(T)={λ∈isoσ(T):0<dimN(T-λI)<∞}.In this paper,we establish for bounded linear operators and their functions the equivalent conditions for which Browder's theorem holds by a new spectrum.

关 键 词：BROWDER定理 谱 算子函数 

分 类 号：O177[理学—数学]