$(\omega)$性质及其摄动

Property $(\omega)$ and Its Perturbations

中文关键词:  $(\omega)$性质  摄动  一致Fredholm指标算子.

英文关键词:property $(\omega)$  perturbation  consistency in Fredholm and index.

中文摘要:

      根据本质逼近点谱的变形与一致Fredholm指标算子定义的谱集, 本文给出了Hilbert空间上有界线性算子$(\omega)$性质摄动的充要条件, 并且研究了$H(P)$算子$(\omega)$性质的摄动.

英文摘要:

      In the note, we establish for a bounded linear operator defined on a Hilbert space the necessary and sufficient conditions for the stability of property $(\omega)$ by means of the variant of the essential approximate point spectrum and the induced spectrum of consistency in Fredholm and index. In addition, the stability of property $(\omega)$ for $H(P)$ operators is considered.