(z)性质与Weyl型定理

Property(z) and Weyl type theorem

称T∈B(X)满足Weyl定理新的变化性质——(z)性质,如果T的上半Weyl谱在T的谱集中的补集恰好为T的逼近点谱中孤立的有限重的特征值全体。讨论了(z)性质与其它Weyl型定理之间的关系,利用变化的本性逼近点谱给出了Banach空间中有界线性算子及其函数演算满足(z)性质的充要条件,考虑了(z)性质的可交换有限秩摄动。

An operator T∈B（ X） defined on a Banach space X satisfies property（ z）,a newvariant of Weyl＇s theorem if the complement in the spectrum σ（ T） of the upper semi-Weyl spectrum is the set of all isolated points of the approximate point spectrum which are eigenvalues of finite multiplicity. In this note,we first study the conditions between property（ z） and other Weyl type theorem,then establish for a bounded linear operator and the calculus defined on a Banach space the sufficient and necessary conditions for which property（ z） holds by means of the variant of essential approximate point spectrum. The perturbation of property（ z） under finite rank operators is considered.