【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(Wn)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.更多还原

【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(Wn) ifσ(T) σ_w(T)=Π(T),where σ(T),σ_w(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(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.更多还原