Positive almost Dunford–Pettis operators and their duality

We study some properties of almost Dunford–Pettis operators and we characterize pairs of Banach lattices for which the adjoint of an almost Dunford–Pettis operator inherits the same property and look at conditions under which an operator is almost Dunford–Pettis whenever its adjoint is.     

Some characterizations of compact operators on Banach lattices

We study the compactness of the class of operators which are AM-compact and semi-compact on Banach lattices and as consequences, we obtain some characterizations of order continuous norms.      

The duality problem for the Class of b-weakly compact operators

We establish necessary and sufficient conditions under which b-weakly compact operators between Banach lattices have b-weakly compact adjoints or operators with b-weakly compact adjoints are themselves b-weakly compact. Also, we give some consequences.