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。
Property(WΠ)and the Property of Topological Uniform Descent for Bounded Linear Operators
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.
NETL
NSTL
万方数据
