A-Weyl's定理和$(WE)$性质的摄动

车雨红^*, 戴磊

Che Yuhong^*, Dai Lei

School of Mathematics and Statistics, Weinan Normal University, Weinan 714099, China

Online:2023-09-28 Published:2023-10-09
Contact: Che Yuhong(1982–), Lecturer, MSc; E-mail:hongmeigui_2022@163.com; cheyuhong@wnu.edu.cn
Supported by:
This work is supported by the Natural Science Foundation of Shannxi Province (No. 2021JM519), 2021 Talent Project of Weinan

Normal University (No. 2021RC16) and 2022 Horizontal Project of Weinan

Normal University (No. 2022HX126)

摘要： 本文研究使有界线性算子的a-Weyl定理和$(WE)$性质都成立的充分必要条件. 同时，研究a-Weyl定理和$(WE)$性质在拟幂零或紧摄动下的稳定性. 作为应用，研究特殊算子的相关稳定性.

关键词: A-Weyl定理, $(WE)$性质, 紧摄动, 拟幂零摄动

Abstract:

In this paper we investigate the necessary and sufficient conditions such that both a-Weyl's theorem and the

property $(WE)$ hold for a bounded linear operator, and study the stability of a-Weyl's theorem and

the property $(WE)$ under quasi-nilpotent

or compact perturbations. As an application, the relative stability of special operators is studied.

Key words: A-Weyl's theorem, Property $(WE)$, Compact perturbation, Quasi-nilpotent perturbation

车雨红, 戴磊. A-Weyl's定理和$(WE)$性质的摄动[J]. 数学理论与应用, 2023, 43(3): 81-94.

Che Yuhong, Dai Lei. A-Weyl's Theorem and the Property $(WE)$ under Perturbations[J]. Mathematical Theory and Applications, 2023, 43(3): 81-94.

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