$(\omega')$性质及其摄动

Property $(\omega')$ and Its Perturbation

中文关键词:  $(\omega')$性质  谱  Weyl型定理.

英文关键词:property $(\omega')$  spectrum  Weyl's theorem.

中文摘要:

      本文定义了Weyl型定理的一种新变化:$(\omega')$性质.利用本质逼近点谱的变形 $\sigma_{1}(\cdot)$和通过一致Fredholm指标算子定义的谱集,给出了Hilbert空间上有界线性算子满足$(\omega')$性质的充要条件.同时$(\omega')$性质的摄动得到了研究.

英文摘要:

      In this note we define the property $(\omega')$, a variant of Weyl's theorem, and establish for a bounded linear operator defined on a Hilbert space the necessary and sufficient conditions for which property $(\omega')$ holds by means of the variant of the essential approximate point spectrum $\sigma_{1}(\cdot)$ and the spectrum defined in view of the property of consistency in Fredholm and index. In addition, the perturbation of property $(\omega')$ is discussed.