Denote a semisimple Banach algebra with an identity e by A. This paper studies the Fredholm, Weyl and Browder spectral theories in a semisimple Banach algebra, and meanwhile considers the properties of the Fredholm element, the Weyl element and the Browder element. Further, for a ∈ A, we give the Weyl’s theorem and the Browder’s theorem for a, and characterize necessary and sufficient conditions that both a and f(a) satisfy the Weyl’s theorem or the Browder’s theorem, where f is a complex-valued function analytic on a neighborhood of σ(a). In addition, the perturbations of the Weyl’s theorem and the Browder’s theorem are investigated.

中文翻译：

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半简单Banach代数中的Weyl定理及其扰动

用A表示标识为e的半简单Banach代数。本文研究了半简单Banach代数中的Fredholm，Weyl和Browder谱理论，同时考虑了Fredholm元素，Weyl元素和Browder元素的性质。此外，对于一个∈甲，我们给予Weyl定理和白劳德定理一个，和表征的充分必要条件，这两个一和˚F（一）满足Weyl定理或白劳德定理，其中˚F是复值函数解析σ（a）。另外，研究了韦尔定理和布朗德定理的摄动。