The Class Of B-Dunford-Pettis Operators On Banach Lattices

Based on the definitions of b-AM-compact operators and b-limited operators,we introduce the classes of b-Dunford-Pettis operators and b-almost limited operators on Banach lattices.Mainly,the sequential characterizations and basic properties of the two classes of operators are discussed.Firstly,we give the concept and equivalent characterizations of b-DunfordPettis operators.By means of the conjugate relation between b-Dunford-Pettis operator and Dunford-Pettis operator,we proved that the domination property is valid for the class of b-Dunford-Pettis operators.The relationship between b-Dunford-Pettis operators and b-AM-compact operators(weakly limited operators,Dunford-Pettis operators,order Dunford-Pettis operators)are also investigated.Secondly,we introduce the class of b-almost limited operators and give the condition under which b-almost limited operators satisfy the domination property.Then we study the relationship between b-almost limited operators and almost limited operators,order-almost limited operators,b-weakly compact operators and b-AMcompact operators.