张量积空间上的强可分算子和弱可分算子  

Strongly and weakly separable operators on tensor product spaces

作　　者：梁文婷[1] 陈峥立[1] 

机构地区：[1]陕西师范大学数学与信息科科学院,陕西西安710062

出　　处：《山东大学学报（理学版）》2016年第4期19-24,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11371012);中央高校基本科研业务资助项目(GK201002006)

摘　　要：引入强可分算子与弱可分算子的概念。称具有形式T=AB的算子T为可分算子;称T为强可分算子,若T可以将所有向量映成可分向量;称可分算子T为弱可分算子,若Tx是可分向量意味着x∈C^n是可分向量。首先给出了当C^nC^n\{0}中可分向量的有限和仍是可分向量时,对应分量组成的向量组秩的刻画。其次分别得到了C^2C^2上的可分算子是强可分的和弱可分的刻画,并分别证明了两个可分算子的和是强可分算子和弱可分算子的充分必要条件。The definitions of strongly separable and weakly separable operators are introduced. Operators of the form T = AB are called separable operators. An operator T is said to be strongly separable if T maps all vectors to separable vectors; and a separable operator T is said to be weakly separable if Tx is separable implies x∈Cnis separable. Firstly,we give out a characterization of the rank of the corresponding components of vectors from C^nC^n\ { 0} when the sum of those finite separable vectors is still separable. Then characterizations of a separable operator being strongly separable and weakly separable are obtaiend,and the necessary and sufficient conditions are given for the sum of two separable operators being strongly separable and weakly separable.

关 键 词：可分算子 强可分算子 弱可分算子 

分 类 号：O177[理学—数学]