Banach格上的几乎L-Dunford-Pettis性质  

Almost L-Dunford-Pettis Property in Banach Lattices

作　　者：陈缘媛 陈金喜[1] 陈滋利[1] CHEN Yuanyuan;CHEN Jinxi;CHEN Zili(College of Mathematics,Southwest Jiaotong University,Chengdu 611756,Sichuan)

机构地区：[1]西南交通大学数学学院,四川成都611756

出　　处：《四川师范大学学报（自然科学版）》2021年第6期767-771,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11701479)

摘　　要：引入几乎L-Dunford-Pettis集,根据几乎L-Dunford-Pettis集定义的启发给出Banach格上的几乎L-Dunford-Pettis性质的定义,研究几乎L-Dunford-Pettis性质与Banach格的某些性质以及算子(不交Dunford-Pettis全连续算子,弱紧算子)之间的关系,并考虑几乎L-Dunford-Pettis性质与弱Dunford-Pettis性质之间的联系.In this paper,we introduce the concept of almost L-Dunford-Pettis sets in Banach lattices,and then give the definition of almost L-Dunford-Pettis property in Banach lattices.A characterization of the almost L-Dunford-Pettis property with respect to some properties of Banach lattices and operators(disjoint DunfordPettis completely continuous,weak compact operators)is given.Finally,we study the relationship between almost L-Dunford-Pettis property and weak DunfordPettis property.

关 键 词：几乎L-Dunford-Pettis集 几乎L-Dunford-Pettis性质 正Dunford-Pettis相对紧性质 不交Dun-ford-Pettis全连续算子 

分 类 号：O177[理学—数学]