Banach格上的无界绝对弱收敛的弱Dunford-Pettis算子

Uaw-w-Dunford-Pettis Operators on Banach Lattices

首先提出一类定义在Banach格上的新算子--无界绝对弱收敛的Dunford-Pettis算子,记作uaw-w-Dunford-Pettis算子,利用构造不交列的技巧给出uaw-w-Dunford-Pettis算子的等价刻画,并给出其中几个相关性质.最后研究该算子与弱Dunford-Pettis算子和M-弱紧算子间的关系.

A new class of operators is proposed,so called uaw-w-Dunford-Pettis operator.The equivalent characterization of the uaw-w-Dunford-Pettis operator is given by using the skills of disjoint sequence,and some of the related properties are given.At last,we study the relationship between uaw-w-Dunford-Pettis operators and weak Dunford-pettis operators(M-weak-compact operators)in this paper.