拟幂零等价算子Weyl定理的稳定性  

The Stability of Weyl′s Theorem for the Quasinilpotent Equivalent Operators

作　　者：梁宏伟[1] 邓未冰[1] 周世璇 

机构地区：[1]河南大学数学与统计学院,河南开封475004 [2]对外经济贸易大学金融学院,北京100029

出　　处：《河南大学学报（自然科学版）》2015年第3期266-268,共3页Journal of Henan University:Natural Science

基　　金：河南省软科学研究项目(142400410924)

摘　　要：线性算子的谱理论,特别是Hilbert空间上Browder定理和Weyl定理在紧摄动下的稳定性问题是目前研究的热点,本文利用拟幂零等价算子的定义及其之间的关系,研究了它们的Browder定理和Weyl定理在紧摄动下的稳定性,并得出它们的稳定性是等价的.The spectral theory of linear operators,especially the stability problem of Browder＇s theorem and Weyl＇s theorem,is presently receiving much attention under compact perturbations in the Hilbert space is a hotspot of research.In this paper,using the property of quasinilpotent equivalent operators,we study the stability of the quasinilpotent equivalent operators of the Browder＇s theorem and Weyl＇s theorem under compact perturbations,and find that their stabilities are equivalent.

关 键 词：拟幂零等价算子 BROWDER定理 WEYL定理 紧摄动 

分 类 号：O177.2[理学—数学]