序极限算子的分解  

Factorization of order limited operators

作　　者：周玉莎[1] 陈滋利[1] 文永明[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3期360-363,共4页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：四川省基础研究项目算子理论及其在系统控制中的应用研究(2010JY0067)

摘　　要：给出了序极限算子的定义以及其序列的等价刻画,同时得到了当值域空间与定义域空间相同时,序极限算子与区间是极限集是等价的.序极限算子满足左乘的性质,并且由序极限算子构成的全体是闭子空间.除此之外,也给出了判定序极限算子的充分不必要条件,并给出结论不是充要条件的反例.序极限算子具有分解性,即可以通过具有序连续范数的Banach格分解,可得到相关结论.This paper gives the definition and characterization of order limited operator, and discusses the basic propellies of or- der limited operators. That is,the set of all order limited operators from Banach Lattice to Banach space is a norm closed vector subspace. Additionally,it is proved that every continuous operator from Banach Lattice to Banach space is order limited operator,but it is not necessary and sufficient. The factorization theorem of order limited operator is obtained through Banach lattice with order continuous norm and related results.

关 键 词：序极限算子 序连续范数 分解性 

分 类 号：O177[理学—数学]