The O-Dunford-Pettis Operators On Banach Lattice

A new kind of operator named O-Dunford-Pettis operator has been proposed in recent years which derived from the concept of Dunford-Pettis set. However, the research about O-Dunford-Pettis operator which just focuses on the domination property, lattice property and AM-compact property is not comprehensive enough for now. This paper will provide more in-depth study of O-Dunford-Pettis operator. The property and duality property of O-Dunford-Pettis operator and the relationship with some special operators like Dunford-Pettis operator, weak Dunford-Pettis operator and almost Dunford-Pettis operator will be discussed.Firstly, we introduce the basic concepts on Banach lattices and some basic theories of special operators to make the foundation for further research.Secondly, we discuss the property of O-Dunford-Pettis operator and some conditions to be an O-Dunford-Pettis operator. Then the duality property of O-Dunford-Pettis operator is also studied in this paper. We find the equivalent conditions between O-Dunford-Pettis operator and its dual operator and what the properties of space shoud have if an operator and its dual operator are all O-Dunford-Pettis operators.Finally, this paper focuses on the relationship between O-Dunford-Pettis operator and Dunford-Pettis operator, weak Dunford-Pettis operator, almost Dunford-Pettis operator. We discuss that in what condition does O-Dunford-Pettis operator coincide with these special operators and what property does the space shoud have if the O-Dunford-Pettis operator is also these special operators.