摘要
本文利用广义Kato性质诱导的谱集,研究了Weyl定理的一种新变形,称其为(h)性质,并证明了(h)性质如何根据该谱集性质得到.同时给出了直和算子T⊕S满足(h)性质的条件.此外,利用该诱导谱集研究了Banach空间上的有界算子T在与T交换的幂有限秩算子扰动下的(h)性质稳定性.
In this paper,by means of the induced spectrum of generalized Kato property,we study a new variant of Weyl's theorem which is called property(h),and show that how property(h)follows from properties of this spectrum.We also give the condition that the direct sum T+S satisfies property(h).In addition,the induced spectrum contributes the stability of property(h),for a bounded operator T acting on a Banach space,under perturbations by power finite rank operators commuting with T.
作者
刘爱芳
郑宇洁
LIU Aifang;ZHENG Yujie(College of Mathematics,Taiyuan University of Technology,Taiyuan,Shanci,030024,P.R.China)
出处
《数学进展》
CSCD
北大核心
2023年第2期339-350,共12页
Advances in Mathematics（China）
基金
Partially supported by NSFC(No.11801397)
China Scholarship Council(No.202006935001)。
关键词
(h)性质
广义Kato型算子
谱
扰动
property(h)
generalized Kato type operators
spectrum
perturbation
