Banach格上的b-几乎Dunford-Pettis算子  

B-almost Dunford-Pettis operators in Banach lattices

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

机构地区：[1]西南交通大学数学学院,四川成都611756

出　　处：《纯粹数学与应用数学》2020年第1期50-57,共8页Pure and Applied Mathematics

基　　金：国家自然科学基金(11701479).

摘　　要：首先给出了Banah格上的b-几乎Dunford-Pettis算子的定义;其次,研究了b-几乎Dunford-Pettis算子的相关性质,如b-几乎Dunford-Pettis算子的等价刻画,构成空间的性质,以及控制性;最后,研究了b-几乎DunfordPettis算子与相关算子(b-弱紧算子,弱紧算子,几乎Dunford-Pettis算子)间的关系.In this paper,we introduce the definition of b-almost Dunford-Pettis operators in Banach lattices.Next,we discuss some properties of b-almost Dunford-Pettis operators.The main properties are the equivalent characterization of b-almost Dunford-Pettis operators,the properties of the space,the domination of b-almost Dunford-Pettis operators.Finally,we study the relationship between b-almost Dunford-Pettis operators and other operators(b-weak compact operator,weak compact operators,almost Dunford-Pettis operators).

关 键 词：b-几乎Dunford-Pettis算子 几乎Dunford-Pettis算子 弱紧算子 序连续范数 

分 类 号：O177[理学—数学]