The approximate Jordan forms of operators on Σ_e^1 type Banach spaces  

作　　者：ZHANG YunNan LIN LiQiong ZHONG HuaiJie 

机构地区：[1]School of Mathematics and Computer Science,Fujian Normal University,Fuzhou 350007,China [2]Mathematics and Information Science College,Hebei Normal University,Shijiazhuang 050016,China [3]College of Mathematics and Computer Science,Fuzhou University,Fuzhou 350002,China

出　　处：《Science China Mathematics》2011年第4期723-740,共18页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.10771034);Tian Yuan Foundation of China (Grant No.10926173);Fujian Natural Science Foundation (GrantNo.2009J05002)

摘　　要：This paper studies the structure of operators on Σ1e type Banach spaces.It solves the problem of the small compact perturbations of operators with connected spectra.Namely,it shows that every operator with a connected spectrum on separable Σ1e type Banach spaces is a small compact perturbation of a strongly irreducible operator.Based on this result,this paper establishes the approximate Jordan forms of operators on Σ1e type Banach spaces with Schauder bases.This paper studies the structure of operators on Σ1e type Banach spaces.It solves the problem of the small compact perturbations of operators with connected spectra.Namely,it shows that every operator with a connected spectrum on separable Σ1e type Banach spaces is a small compact perturbation of a strongly irreducible operator.Based on this result,this paper establishes the approximate Jordan forms of operators on Σ1e type Banach spaces with Schauder bases.

关 键 词：Σ1e type Banach spaces strongly irreducible operators operators with connected spectra approximate Jordan forms 

分 类 号：O177.2[理学—数学] O175[理学—基础数学]