Banach格上的b-L-弱紧算子  

b-L-weakly compact operators on Banach lattices

作　　者：李辉[1] 陈滋利[1] 陈金喜[1] 

机构地区：[1]西南交通大学数学学院,四川成都610031

出　　处：《西南民族大学学报（自然科学版）》2015年第2期224-228,共5页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：国家自然科学基金(11301285)

摘　　要：首先提出了一类定义在Banach lattice上的新算子——b-L-弱紧算子,并对其相关性质进行了研究,如每个有界线性算子为b-L-弱紧算子的空间条件、b-L-弱紧算子构成空间的性质、b-L-弱紧算子的共轭性和控制性;其次研究了在一定的空间条件下b-L-弱紧算子是L-弱紧算子或M-弱紧算子的充分或必要条件;最后研究了当E和F均有序连续范数时,序L-弱紧算子是b-L-弱紧算子的充分必要条件.A new class of operators is proposed, so called b-L-weakly compact operator, and some properties of it are discussed. The main properties are the space conditions for every linearly bounded operator being a b-L-weakly compact operator, the properties of the space which is formed by all b-L-weakly compact operators, the duality of the operator and domination. The b-L-weakly compact operator being L-（M-）weakly compactness is considered and some sufficient or necessary conditions are gained. The necessary and sufficient conditions are obtained that every order L-weakly compact operator is b-L-weakly compact when E and F have order continuous norm.

关 键 词：BANACH格 L-弱紧算子 M-弱紧算子 b-L-弱紧算子 序L-弱紧算子 

分 类 号：O177.5[理学—数学]