Unbounded absolutely weak Dunford–Pettis operators

Abstract

In the present article, we expose various properties of unbounded absolutely weak Dunford–Pettis andunbounded absolutely weak compact operators on a Banach lattice E. In addition to their topological and latticeproperties, we investigate relationships between M-weakly compact operators, L-weakly compact operators, and orderweakly compact operators with unbounded absolutely weak Dunford–Pettis operators. We show that the square of anypositive uaw-Dunford–Pettis (M-weakly compact) operator on an order continuous Banach lattice is compact. Manyexamples are given to illustrate the essential conditions.