有界线性算子的(W_(Π))性质和拓扑一致降标性质  

Property(W_(Π))and the Property of Topological Uniform Descent for Bounded Linear Operators

作　　者：苏卓媛 窦艳妮[1] SU Zhuo-yuan;DOU Yan-ni(School of Mathematics and Statistics,Shaanxi Normal University,Xi'an 710062,China)

机构地区：[1]陕西师范大学数学与统计学院,陕西西安710062

出　　处：《数学的实践与认识》2024年第2期211-218,共8页Mathematics in Practice and Theory

基　　金：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)。

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)σ_(w)(T)=Π(T),则称算子T∈B(H)满足(W_(Π))性质,其中σ(T),σ_(w)(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(W_(Π))性质,并对算子函数的(W_(Π))性质以及(W_(Π))性质的Riesz摄动进行研究.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(Wn)if σ(T)\σ_(w)(T)=Π(T),where σ(T),σ_(w)(T)and II(T)denote the spectrum,Weyl spectrum and the set of all poles of T respectively.In this note,we describe the characteristic of property(W_(Π))using the property of topological uniform descent.In additional,we explored the property(W_(Π))of the functions of linear bounded operators and the property(W_(Π))under Riesz perturbations.

关 键 词：(W_(Π))性质 拓扑一致降标 谱 

分 类 号：O177[理学—数学]