华东师范大学学报（自然科学版） >

2025 , Vol. 2025 >Issue 1: 13 - 27

DOI: https://doi.org/10.3969/j.issn.1000-5641.2025.01.002

数学

有界线性算子的Fa-Weyl定理与a-Weyl定理

  • 李偲萌 ,
  • 张邺 ,
  • 曹小红
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  • 陕西师范大学 数学与统计学院, 西安　710119
张　邺, 男, 副教授, 研究方向为算子理论与算子代数. E-mail: zhangye@snnu.edu.cn

收稿日期: 2023-11-28

  网络出版日期: 2025-01-20

基金资助

国家自然科学基金(11971283)

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华东师范大学学报期刊社, 2025, 版权所有，未经授权，不得转载、摘编本刊文章，不得使用本刊的版式设计。
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Fa-Weyl’s theorem and a-Weyl’s theorem for bounded linear operators

  • Simeng LI ,
  • Ye ZHANG ,
  • Xiaohong CAO
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  • School of Mathematics and Statistics, Shaanxi Normal University, Xi’an　710119, China

Received date: 2023-11-28

  Online published: 2025-01-20

Copyright

, 2025, Copyright reserved © 2025.
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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.

关键词： Fa-Weyl 定理; a-Weyl 定理; 摄动; 谱

本文引用格式

李偲萌 , 张邺 , 曹小红 . 有界线性算子的Fa-Weyl定理与a-Weyl定理[J]. 华东师范大学学报（自然科学版）, 2025 , 2025(1) : 13 -27 . DOI: 10.3969/j.issn.1000-5641.2025.01.002

Abstract

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.

Key words： Fa-Weyl’s theorem; a-Weyl’s theorem; perturbation; spectrum

参考文献

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