正几乎弱算子的性质  

On the Properties of the Positive Almost Weak Operators

作　　者：刘梦新[1] 邓洋[1] 

机构地区：[1]西南交通大学数学学院,四川成都611756

出　　处：《绵阳师范学院学报》2016年第8期44-48,共5页Journal of Mianyang Teachers＇ College

基　　金：国家自然科学基金(11301285);中央高校基本科研业务费创新项目(SWJTU11CX54)

摘　　要：为了更方便的研究Dunford-Pettis算子及几乎极限算子的相关性质,文章给出了几乎弱算子的定义,以此建立者两种算子之间的桥梁.本文利用了构造不交列的技巧,用序列的形式给出了正几乎弱算子的刻画.在给定的条件下,得出了正几乎弱算子的共轭算子还是几乎弱算子.相反的,本文给出了条件使得当一个算子的共轭算子是几乎弱算子时,它自己也是几乎弱算子.最后,利用构造特殊算子的技巧,给出了使得每个几乎弱Dunford-Pettis算子都是几乎弱算子的等价条件.In order to study the properties of the Dunford-Pettis operator and almost the limit operator,the paper gives the definition of almost weak operator,which can serve as the bridge between the two operators. We first give a characterization of positive almost weak operator by using the skills of disjoint sequence. Then,we study under what conditions their adjoint operators are still almost weak. Also on the converse,under some conditions,there are still almost weak when their adjoint operators are almost weak. At last,we use the technique of constructing special operators,and give the equivalent conditions for almost every weakly Dunford-Pettis operator to be almost weak operator.

关 键 词：巴拿赫格 几乎弱算子 弱零列 不交列 

分 类 号：O177[理学—数学]