算子函数的Weyl定理及其稳定性  

Weyl’s Theorem for Functions of Operators and Stability

作　　者：杨莉莉[1] 曹小红 Li Li YANG;Xiao Hong CAO(School of Mathematics and Statistics,Shaanxi Normal Uniuersity,Xi'an 710119,P.R.China)

机构地区：[1]陕西师范大学数学与统计学院,西安710119

出　　处：《数学学报（中文版）》2022年第1期67-76,共10页Acta Mathematica Sinica：Chinese Series

基　　金：陕西师范大学中央高校基本科研业务费资助项目(GK202007002)。

摘　　要：设H是无限维复Hilbert空间,B(H)表示H上的有界线性算子全体构成的集合.本文对B(H)中使得f(T)满足Weyl定理的算子进行刻画,其中f是T的谱集的某个邻域上的解析函数.同时,也对算子函数的Weyl定理及算子Weyl定理的摄动之间的关系进行了讨论.Let H be a complex infinite dimensional Hilbert space.B(H)denotes the algebra of all bounded linear operators on H.In this paper,we characterize the operators in B(H)for which f(T)satisfies Weyl’s theorem,where f denotes the analytic function on some neighbourhood of the spectrum of T.Also,the relationships between Weyl’s theorem for functions of operators and the stability of Weyl’s theorem are explored.

关 键 词：WEYL定理 算子函数 稳定性 

分 类 号：O177.2[理学—数学]