Banach格上的b-Dunford-Pettis算子  

B-Dunford-Pettis operators on Banach lattices

作　　者：李娇娇 陈金喜[1] 陈滋利[1] Li Jiaojiao;Chen Jinxi;Chen Zili(College 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》2017年第5期513-521,共9页Pure and Applied Mathematics

基　　金：国家自然科学基金(11301285)

摘　　要：为了进一步研究Banach格上算子的性质,受b-序有界集和Dunford-Pettis集定义的启发,给出了b-Dunford-Pettis算子的定义,研究了该算子与b-AM-紧算子(Dunford-Pettis全连续算子,弱极限算子,序Dunford-Pettis算子)间的关系;利用b-Dunford-Pettis算子与Dunford-Pettis算子的共轭关系,证明了b-Dunford-Pettis算子满足控制性.For the further study of the property of operators on Banach lattices,we give the de_niton of b-Dunford-Pettis operator in light of the de_nition of b-order bounded set and Dunford-Pettis set,and study the relationship between b-Dunford-Pettis operator and b-AM-compact operator(Dunford-Pettis completely continuous operator,weakly limited operator,order Dunford-Pettis operator)in this paper;By means of the conjugate relation between b-Dunford-Pettis operator and Dunford-Pettis operator,it was proved that b-Dunford-Pettis operator has the dominated property.

关 键 词：b-Dunford-Pettis算子 b-AM-紧算子 弱极限算子 相对紧Dunford-Pettis性质 

分 类 号：O177[理学—数学]