On Weyl's Theorem for Functions of Operators

被引：0

作者：

Jiong DONG ^{[1
]}

Xiao Hong CAO ^{[1
]}

Lei DAI ^{[2
]}

机构：

[1] School of Mathematics and Information Science,Shaanxi Normal University

[2] College of Mathematics and Physics,Weinan Normal University

来源：

Acta Mathematica Sinica,English Series | 2019年 / 08期

基金：

中央高校基本科研业务费专项资金资助; 中国国家自然科学基金;

关键词：

Spectrum; Weyl’s theorem; functions of operators; compact perturbation;

D O I：

暂无

中图分类号：

O177.1 [希尔伯特空间及其线性算子理论];

学科分类号：

070104 ;

摘要：

Let H be a complex separable infinite dimensional Hilbert space. In this paper, a variant of the Weyl spectrum is discussed. Using the new spectrum, we characterize the necessary and sufficient conditions for both T and f(T) satisfying Weyl’s theorem, where f ∈ Hol(σ(T)) and Hol(σ(T)) is defined by the set of all functions f which are analytic on a neighbourhood of σ(T) and are not constant on any component of σ(T). Also we consider the perturbations of Weyl’s theorem for f(T).

引用

页码：1367 / 1376

页数：10

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