有界线性算子的a-Weyl定理的判定

doi:10.6040/j.issn.1671-9352.0.2019.729

《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (10): 88-94.doi: 10.6040/j.issn.1671-9352.0.2019.729

有界线性算子的a-Weyl定理的判定

冯高慧子,曹小红^*

陕西师范大学数学与信息科学学院, 陕西西安 710119

出版日期:2020-10-20 发布日期:2020-10-07
作者简介:冯高慧子(1995— ), 女, 硕士研究生, 研究方向为算子理论. E-mail:635003220@qq.com*通信作者简介:曹小红(1972— ), 女, 教授, 博士生导师, 研究方向为算子理论. E-mail:xiaohongcao@snnu.edu.cn
基金资助:
国家自然科学基金资助项目(11471200)

Judgement of a-Weyls theorem for bounded linear operators

FENG-GAO Hui-zi, CAO Xiao-hong^*

School of Mathematics and Information Science, Shaanxi Normal University, Xian 710119, Shaanxi, China

Online:2020-10-20 Published:2020-10-07

摘要/Abstract

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。若σa(T)\σ_ea(T)=π^a₀₀(T),称算子T∈B(H)满足a-Weyl定理,其中σa(T)、σ_ea(T)分别表示T的逼近点谱、本质逼近点谱, π^a₀₀(T)={λ∈iso σa(T):0<n(T-λI)<∞}。讨论有界线性算子及其算子函数满足a-Weyl定理的新的判定方法, 并讨论相关谱集的谱映射定理。

关键词: a-Weyl定理, 逼近点谱, 本质逼近点谱

Abstract: 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 the a-Weyls theorem if σ_a(T)\σ_ea(T)=π^a00(T), where σ_a(T) and σ_ea(T) denote the approximate point spectrum and essential approximate point spectrum respectively, and π^a00(T)={λ∈iso σ_a(T):0<n(T-λI)<∞}. A new judgement for the a-Weyls theorem for operators and operator functions is given. Also, the spectrum mapping theorem related to spectrum is considered.

Key words: a-Weyls theorem, approximate point spectrum, essential approximate point spectrum

中图分类号:

O177.1

冯高慧子,曹小红. 有界线性算子的a-Weyl定理的判定[J]. 《山东大学学报(理学版)》, 2020, 55(10): 88-94.

FENG-GAO Hui-zi, CAO Xiao-hong. Judgement of a-Weyls theorem for bounded linear operators[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(10): 88-94.

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有界线性算子的a-Weyl定理的判定

Judgement of a-Weyls theorem for bounded linear operators

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