The purpose of this paper is to study mean ergodic theorems concerning continuous or positive operators taking values in Jordan-Banach weak algebras and Jordan C＊-algebras, making use the topological and order struct...The purpose of this paper is to study mean ergodic theorems concerning continuous or positive operators taking values in Jordan-Banach weak algebras and Jordan C＊-algebras, making use the topological and order structures of the corresponding spaces. The results are obtained applying or extending previous classical results and methods of Ayupov, Carath6odory, Cohen, Eberlein, Kakutani and Yosida. Moreover, this results can be applied to continious or positive operators appearing in diffusion theory, quantum mechanics and quantum 13robabilitv theory.展开更多
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
文摘The purpose of this paper is to study mean ergodic theorems concerning continuous or positive operators taking values in Jordan-Banach weak algebras and Jordan C＊-algebras, making use the topological and order structures of the corresponding spaces. The results are obtained applying or extending previous classical results and methods of Ayupov, Carath6odory, Cohen, Eberlein, Kakutani and Yosida. Moreover, this results can be applied to continious or positive operators appearing in diffusion theory, quantum mechanics and quantum 13robabilitv theory.
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.
