Banach格上的b-AM-紧算子(英文)  

b-AM-compact Operators on Banach Lattices

作　　者：程娜[1] 陈滋利[1] 

机构地区：[1]西南交通大学数学学院,成都610031

出　　处：《工程数学学报》2010年第4期753-756,共4页Chinese Journal of Engineering Mathematics

摘　　要：本文对Banach格上的b-AM-紧算子进行了描述,得到了如下三个结论:1)如果Banach格F是无限维的,则E是KB-空间当且仅当每个从E到F的AM-紧算子是b-AM-紧算子。2)Banach格E是离散的KB-空间当且仅当每个从E到F的连续算子是b-AM-紧算子。3)如果E是离散的,则每个从E到F的b-弱紧算子是b-AM-紧算子。其次给出了b-AM-紧算子的控制性质,得到如下两个结论:1)如果E和F是两个Banach格,算子S,T:E→F满足0≤S≤T且T是b-AM-紧算子,则算子S是b-AM-紧算子当且仅当F具有序连续范数或者E是离散空间。2)如果S,T是从E到F的算子满足0≤S≤T,如果T是b-AM-紧算子,则S2也是b-AM-紧算子。Several characterizations of b-AM-compact operators are considered in this paper, we show that： 1） If F is an infinite-dimensional Banach lattice, then E is a KB-space if and only if every AM-compact operator from E into F is b-AM-compact. 2） The Banach lattice E is a discrete KB-space if and only if every continuous operator from E into Banach lattice F is b-AM-compact. 3） If the topological dual E is discrete, then every b-weakly compact operator from Banach E into Banach space X is b-AM-compact. Moreover, following prop- erties about the problems of domination in the class of positive b-AM-compact operators are established： 1） If E and F are two Banach lattices, then for all operators S, T ： E → F such that 0 ≤ S ≤ T and T is b-AM-compact, the operator S is b-AM-compact if and only if the norm of F is order continuous or E is discrete. 2） If S, T are two operators from E into F with 0 ≤ S ≤ T, if T is b-AM-compact, then S2 is likewise b-AM-compact.

关 键 词：BANACH格 b-AM-紧算子 

分 类 号：O177.2[理学—数学]