The Properties And Applications Of Dunford-Pettis Set

This paper investigates the KB-space, bi-sequence property, the characterization of Banach spaces in which Dunford-Pettis sets are relatively compact by Dunford-Pettis sets and its properties.The note gives the sufficient and necessary conditions of the Banach lattices which dual lattices are KB-spaces. It introduces weak bi-sequence property by using the definition of bi-sequence property. Meanwhile, it introduces two kinds of operators, that are almost weakly Dunford-Pettis operator and Dunford-Pettis completely continuous operator, which properties are studied and used to characterize the weak bi-sequence property and the Banach spaces in which Dunford-Pettis sets are relatively compact, respectively. It investigates the sufficent conditions of DPrcP of some classical operator spaces by using obtained theory about DPrcP.