Uaw-w-dunford-pettis Operator On Banach Lattices

Based on the definitions of unbounded absolute weak Dunford-Pettis operator and weak Dunford-Pettis operator,we introduce the classes of uaw-w-Dunford-Pettis operator on Banach lattices.This paper mainly discusses the basic properties of these operators and their relations with other operators.Firstly,if the Banach lattice E has a conjugate space E~′ordered continuous norm,the equivalent characterization of uaw-w-Dunford-Pettis operator is given.The uaw-w-Dunford-Pettis operator is characterized by some techniques of disjoint sequence.Second,this paper studies the relationship between the uaw-w-Dunford-Pettis operator and other special operators,In the condition that the Banach lattice E~′has a sequential con-tinuous norm and the Banach lattice F isσ-Dedekind complete,obtained the necessary and sufficient conditions for each positive uaw-w-Dunford-Pettis operator to be a uaw-Dunford-Pettis operator.The relationship between uaw-w-Dunford-Pettis operator and Dunford-Pettis operator,weak Dunford-Pettis operator and M-compact operator is discussed.At last,this paper proposes the classes of uaw-uaw-Dunford-Pettis operator on Banach lattices and studies Some properties of this operator and the relationship between it and related operators.