# Article

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Keywords:
almost weak\$^{\star}\$ Dunford-Pettis operator; almost Dunford-Pettis operator; weak Dunford-Pettis\$^{\star}\$ property; positive Schur property; order continuous norm
Summary:
In this paper, we introduce and study the class of almost weak\$^{\star}\$ Dunford-Pettis operators. As consequences, we derive the following interesting results: the domination property of this class of operators and characterizations of the wDP\$^{\star}\$ property. Next, we characterize pairs of Banach lattices for which each positive almost weak\$^{\star}\$ Dunford-Pettis operator is almost Dunford-Pettis.
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