Weak* Dunford-Pettis Operators On Banach Lattices

The weak* Dunford-Pettis operator is a kind of special operators on Banach lattice. It is an extention of the Dunford-Pettis operator. The weak* Dunford-Pettis operator is closly linked to the compact operator and the weakly compact operator, which has the great research value. By using the skills of disjoint sequence,we depict the weak* Dunford-Pettis operator. Furtherly, we discuss its basic property and the relation with the Dunford-Pettis operators and M-weakly compact operators.The main results:1. We introduce the basic properties of the weak* Dunford-Pettis operator. For instance, its controlling and the structure. We get some conclusions. These are prepared for introducing and further reseaching the weak* Dunford-Pettis operator.2. Some space property of the weak* Dunford-Pettis opertor is studied. First, we give a characterization of weak* Dunford-pettis operator by using the skills of disjoint sequence. Second, establishing sufficent space conditions under which each operator between Banach latties is weak* Dunford-Pettis.3. The relation between the weak* Dunford-Pettis opertor and other special operators is introduced. Each weak* Dunford-Pettis operator has sufficient condition for the M - weak compact operator. At the same time, we discuss the relation with the Dunford-Pettis operator and compact operator.