Characterization of Banach Lattices Whose Biduals Have the Positive Schur Property via Second Adjoints of Operators

The core message of this article is to characterize Banach lattices whose biduals have the positive Schur property by means of second adjoints of operators on the Banach lattice being almost Dunford-Pettis. The authors also extend known results on conditions for the adjoint and second adjoint of positive almost Dunford-Pettis operators to be almost Dunford-Pettis.