### On the class of positive almost weak${}^{\u2606}$ Dunford-Pettis operators

Abderrahman Retbi (2015)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we introduce and study the class of almost weak${}^{\u2606}$ Dunford-Pettis operators. As consequences, we derive the following interesting results: the domination property of this class of operators and characterizations of the wDP${}^{\u2606}$ property. Next, we characterize pairs of Banach lattices for which each positive almost weak${}^{\u2606}$ Dunford-Pettis operator is almost Dunford-Pettis.