中文摘要：

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.

英文摘要：

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.