Browder定理和Weyl定理(英文)

Browder's Theorem and Weyl's Theorem

中文关键词:  Browder定理  Weyl定理  谱

英文关键词:Browder's theorem  Weyl's theorem  spectrum.

中文摘要:

      本文通过定义两个新的谱集,给出了Browder定理和Weyl定理对算子T以及f(T)成立的充要条件,其中f∈H(σ(T)),H(σ(T))表示在谱集σ(T)的开邻域上解析的函数的全体。

英文摘要:

      In this paper, by defining two new spectral sets, we give the necessary and sufficient conditions for Browder's theorem and Weyl's theorem for bounded linear operator T and f(T), where f∈H(σ(T)) and H(σ(T)) denotes the set of all analytic functions on an open neighborhood of σ(T).