Some characterizations of almost Dunford–Pettis operators and applications

This paper attempts to deal with some characterizations of almost Dunford–Pettis operators from a Banach lattice into a Banach space. It also discusses some of the consequences derived from this study. As an application, we generalize some results of Meyer-Nieberg on the duality between semi-compact operators and order weakly compact operators.     

Some properties of the class of positive Dunford-Pettis operators

We characterize Banach lattices for which each positive Dunford-Pettis operator is M-weakly compact (resp. L-weakly compact) and we give some consequences.     

Some properties of almost L-weakly and almost M-weakly compact operators

Positivity - In this paper, we investigate necessary and sufficient conditions under which compact operators between Banach lattices must be almost L-weakly compact (resp. almost M-weakly compact)....     

On the weak compactness of b-weakly compact operators

We characterize Banach lattices on which the class of b-weakly compact operators coincides with that of weakly compact operators.     

Compactness of L-weakly and M-weakly compact operators on Banach lattices

We investigate conditions under which L-weakly compact operators and M-weakly compact operators must be compact.     

Some results on almost L-weakly and almost M-weakly compact operators

Positivity - We introduce and study a new topology on trees, that we call the countably coarse wedge topology. Such a topology is strictly finer than the coarse wedge topology and it turns every...     

Some Properties of the Class of b-Weakly Compact Operators

We establish several characterizations of b-weakly compact operators one of them is similar to that established by Meyer-Nieberg for order weakly compact operators.     

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.     

Characterization of the order weak compactness of semi-compact operators

We study the relation between the class of semi-compact operators and the class of order weakly compact operators and we give some interesting consequences.