AM-compactness of positive Dunford-Pettis operators on Banach lattices (Q2467948)

The authors characterize Banach lattices \(E, F\) where each positive order weakly compact operator from \(E\) into \(F\) is a Dunford-Pettis operator. They further give a characterization of Banach lattices \(E,F\) where each positive Dunford-Pettis operator from \(E\) into \(F\) is AM-compact. They also consider the converse of the last theorem.