Some properties of weak Banach-Saks operators

summary:We establish necessary and sufficient conditions under which weak Banach-Saks operators are weakly compact (respectively, {\rm L}-weakly compact; respectively, {\rm M}-weakly compact). As consequences, we give some interesting characterizations of order continuous norm (respectively, reflexive Banach lattice)

On the class of U-Dunford-Pettis operators

We introduce a new class of operators “DPu(E,Y )” which lives between the class of Dunford-Pettis, the class of AM-compact operators and that of order weakly compact “Lowc(E,Y )”, more precisely we have “DP(E,Y ) ⊂ DPu(E,Y) ⊂ Lowc(E,Y)" and “AMcp(E,Y) ⊂ DPu(E,Y) ⊂ Lowc(E,Y):, where DP(E,Y), AMcp(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