On the class of U-Dunford-Pettis operators

Abstract

We introduce a new class of operators “DP_u(E,Y )” which lives between the class of Dunford-Pettis, the class of AM-compact operators and that of order weakly compact “L_owc(E,Y )”, more precisely we have “DP(E,Y ) ⊂ DP_u(E,Y) ⊂ L_owc(E,Y)" and “AMcp(E,Y) ⊂ DP_u(E,Y) ⊂ L_owc(E,Y):, where DP(E,Y), AM_cp(E,Y) denote the class of Dunford-Pettis operators, AM-compact operators, respectively. And we study some of its properties, like the domination problem and the relations between other classes of operators.