On the Class of Absolutely Weakly Compact Operators

In this paper, we introduce a new class of operators between Banach space and Banach lattice called absolutely weakly compact operators, which lies between the classical classes of compact operators and weakly compact operators. We provide a precise characterization of this class of operators and explore their relations with other notable classes of operators. In addition, we present a solution to the domination problem associated with these operators and discuss the duality problem associated with this new class, detailing the implications of our results.