拓扑一致降标与Weyl定理的摄动

数学物理学报 ›› 2015, Vol. 35 ›› Issue (2): 324-331.

拓扑一致降标与Weyl定理的摄动

崔苗苗, 曹小红

陕西师范大学数学与信息科学学院西安 710062

收稿日期:2013-07-30 修回日期:2014-10-30 出版日期:2015-04-25 发布日期:2015-04-25
通讯作者: 曹小红 E-mail:xiaohongcao@snnu.edu.cn
作者简介:崔苗苗,E-mail:cuiye@snnu.edu.cn
基金资助:
国家自然科学基金(11371012,11471200)和中央高校基本科研业务费专项基金(GK201301007)资助

Topological Uniform Descent and the Perturbation of Weyl's Theorem

Cui Miaomiao, Cao Xiaohong

College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062

Received:2013-07-30 Revised:2014-10-30 Online:2015-04-25 Published:2015-04-25

摘要/Abstract

摘要：

若σ(T)\σ_w(T)⊆π₀₀(T), 则称算子T满足Browder定理, 其中σ(T)和σ_w(T)分别表示算子T的谱和Weyl 谱, 且π₀₀(T)={λ∈isoσ(T);0N(T-λI)< ∞}. 若σ(T)\σ_w(T)=π₀₀(T), 则称T满足Weyl定理. 该文利用拓扑一致降标域的特征, 研究了Browder定理在紧摄动下的稳定性,并且给出了Browder定理的紧摄动具有稳定性的算子的特征.

关键词: Browder定理, 紧摄动, 拓扑一致降标

Abstract:

An operator T is said to satisfy Browder's theorem if σ(T)\σ_w(T)⊆π₀₀(T), where σ(T) and σ_w(T) denote the spectrum and the Weyl spectrum respectively, and π₀₀(T)={λ∈isoσ(T);0N(T-λI)< ∞}. If σ(T)\σ_w(T)=π₀₀(T), we say T satisfies Weyl's theorem. Using the characteristics of Topological uniform descent domain, the stability of Browder's theorem under compact perturbations is investigated, and those operators which have this stability are characterized.

Key words: Browder's theorem, Compact perturbations, Topological uniform descent

中图分类号:

O177.2

崔苗苗, 曹小红. 拓扑一致降标与Weyl定理的摄动[J]. 数学物理学报, 2015, 35(2): 324-331.

Cui Miaomiao, Cao Xiaohong. Topological Uniform Descent and the Perturbation of Weyl's Theorem[J]. Acta mathematica scientia,Series A, 2015, 35(2): 324-331.