The Weyl’s Theorem and Its Perturbations in Semisimple Banach Algebra  

作　　者：Ying Ying KONG Li Ning JIANG Yan Xun REN 

机构地区：[1]School of Mathematics and Statistics,Beijing Institute of Technology,Beijing 100081,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2021年第5期675-688,共14页数学学报（英文版）

基　　金：Supported by NSFC(Grant No.11871303)。

摘　　要：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 ofσ(a).In addition,the perturbations of the Weyl’s theorem and the Browder’s theorem are investigated.

关 键 词：Semisimple Banach algebra Fredholm element Browder element Weyl’s theorem perturbation 

分 类 号：O177.2[理学—数学]