有界线性算子的Fa-Weyl定理与a-Weyl定理  

Fa-Weyl’s theorem and a-Weyl’s theorem for bounded linear operators

作　　者：李偲萌 张邺[1] 曹小红 LI Simeng;ZHANG Ye;CAO Xiaohong(School of Mathematics and Statistics,Shaanxi Normal University,Xi’an 710119,China)

机构地区：[1]陕西师范大学数学与统计学院,西安710119

出　　处：《华东师范大学学报(自然科学版)》2025年第1期13-27,共15页Journal of East China Normal University(Natural Science)

基　　金：国家自然科学基金(11971283)。

摘　　要：Fa-Weyl定理和a-Weyl定理是Weyl定理的两种变形,Weyl型定理的研究对于谱理论研究十分重要.通过定义新的谱集,给出了在Hilbert空间上的有界线性算子T同时满足Fa-Weyl定理和a-Weyl定理的等价条件.此外,还讨论了算子T在有限秩摄动下的Fa-Weyl定理和a-Weyl定理.Both Fa-Weyl’s theorem and a-Weyl’s theorem are the variants of Weyl’s theorem.The study of Weyl’s type theorems is very important for spectral theory.By defining a new spectral set in this paper,sufficient and necessary conditions for a bounded linear operator T definded on a Hilbert space to satisfy the Fa-Weyl’s theorem and the a-Weyl’s theorem are established.In addition,we discuss the Fa-Weyl’s theorem and the a-Weyl’s theorem of bounded linear operator T under a finite rank perturbation.

关 键 词：Fa-Weyl定理 a-Weyl定理 摄动 谱 

分 类 号：O177.2[理学—数学]