Summary: In this paper, we introduce and study the class of almost weak\(^*\) Dunford-Pettis operators. As consequences, we derive the following interesting results: the domination property of this class of operators and characterizations of the wDP\(^*\) property. Next, we characterize pairs of Banach lattices for which each positive almost weak\(^*\) Dunford-Pettis operator is almost Dunford-Pettis.
Editorial remark: Almost identical results were previously obtained in [A. Elbour et al., Quaest. Math. 38, No. 6, 817–827 (2015; Zbl 1406.46011)].