Abderrahman Retbi
On the class of positive almost weak$^{\star}$ Dunford-Pettis operators

Comment.Math.Univ.Carolin. 56,3 (2015) 347-354.

Abstract: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.

Keywords: almost weak$^{\star}$ Dunford-Pettis operator; almost Dunford-Pettis operator; weak Dunford-Pettis$^{\star}$ property; positive Schur property; order continuous norm

DOI: DOI 10.14712/1213-7243.2015.128
AMS Subject Classification: 46A40 46B40

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