(ω1)性质与单值扩张性质

Property （ω1） and the single-valued extension property

称有界线性算子 T满足(ω1)性质,如果T的上半Weyl谱在它的逼近点谱中的补集包含在它的谱集中孤立的有限重的特征值的全体中。根据单值扩张性质定义了一种新的谱集,利用该谱集给出了Hilbert空间中有界线性算子满足(ω1)性质的充分必要条件。作为应用,给出了亚(或超)循环算子类满足(ω1)性质的等价刻画。

A bounded linear operator T satisfies property(ω1), if the complement in the approximate point spectrum σa(T)of the upper semi-Weyl spectrum σea(T)is contained in the set of all isolated points of the spectrum σ(T)which are finite eigenvalues. In this paper, by means of the new spectrum defined in view of the single-valued extension property, the sufficient and necessary conditions for a bounded linear operator defined on a Hilbert space satisfying the property(ω1)are established. As an application, the property(ω1)for hypercyclic(or supercyclic)operators are characterised.