有界线性算子的(WΠ)性质和拓扑一致降标性质
Property(WΠ)and the Property of Topological Uniform Descent for Bounded Linear Operators
苏卓媛 1窦艳妮1
作者信息
- 1. 陕西师范大学数学与统计学院,陕西 西安 710062
- 折叠
摘要
设H为无限维复可分的Hilbert空间,B(H)为H上有界线性算子的全体.若有 σ(T)\σω(T)=Π(T),则称算子 T ∈ B(H)满足(WΠ)性质,其中 σ(T),σw(T),Π(T)分别表示算子T的谱、Weyl谱,以及T的所有极点构成的集合.借助拓扑一致降标性质刻画有界线性算子的(WΠ)性质,并对算子函数的(WΠ)性质以及(WΠ)性质的Riesz摄动进行研究.
Abstract
Let H be an infinite dimensional separable complex Hilbert space and B(H)be the algebra of all bounded linear operators on H.T ∈ B(H)satisfies the property(WΠ)ifσ(T)\ σω(T)=Π(T),where σ(T),σω(T)and Π(T)denote the spectrum,Weyl spectrum and the set of all poles of T respectively.In this note,we describe the characteristic of property(WΠ)using the property of topological uniform descent.In additional,we explored the property(WΠ)of the functions of linear bounded operators and the property(WΠ)under Riesz perturbations.
关键词
(WΠ)性质/拓扑一致降标/谱Key words
property(WΠ)/topological uniform descent/spectrum引用本文复制引用
基金项目
国家自然科学基金(12061031)
陕西省自然科学基础研究计划项目(2021JM-189)
出版年
2024
NETL
NSTL
万方数据