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 connecte...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.展开更多
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)
文摘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.
