算子函数演算的广义Weyl定理

吉林大学学报(理学版)

算子函数演算的广义Weyl定理

赵玲玲^1, 曹小红²

1. 防灾科技学院基础课教学部, 河北三河 065201； 2. 陕西师范大学数学与信息科学学院, 西安 710119

收稿日期:2016-10-19 出版日期:2017-09-26 发布日期:2017-09-26
通讯作者: 曹小红 E-mail:xiaohongcao@snnu.edu.cn

Generalized Weyl’s Theorem for Functional Calculus of Operators

ZHAO Lingling^1, CAO Xiaohong²

1. Department of Fundamental Courses, Institute of Disaster Prevention, Sanhe 065201, Hebei Province, China;2. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710119, China

Received:2016-10-19 Online:2017-09-26 Published:2017-09-26
Contact: CAO Xiaohong E-mail:xiaohongcao@snnu.edu.cn

摘要/Abstract

摘要： 考虑Weyl定理的一种变型广义Weyl定理, 通过定义一种新谱集, 利用该谱集给出算子T及其函数演算满足广义Weyl定理的充要条件, 得到了算子T及其函数满足广义Weyl定理的新判别方法.

关键词: 广义Weyl定理, B-Weyl谱, Weyl定理

Abstract: We considered a variant of the Weyl’s theorem: the generalized Weyl’s theorem. By defining a new spectral set, we gave sufficient and necessary conditions for the operator T and its functional calculus to satisfy the generalized Weyl’s theorem by using the spectral set. We obtained a new discriminant for T and its functional calculus to satisfy the generalized Weyl’s theorem.

Key words: Weyl’s theorem, generalized Weyl’s theorem, B-Weyl’s spectrum

中图分类号:

O177.2

赵玲玲, 曹小红. 算子函数演算的广义Weyl定理[J]. 吉林大学学报(理学版), 2017, 55(05): 1129-1134.

ZHAO Lingling, CAO Xiaohong. Generalized Weyl’s Theorem for Functional Calculus of Operators[J]. Journal of Jilin University Science Edition, 2017, 55(05): 1129-1134.