Almost L-Dunford-Pettis sets in Banach lattices and its applications

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Hacettepe Journal of Mathematics and Statistics
Volume:49 Issue:2
Almost L-Dunford-Pettis sets in Banach lattices and its applications

Almost L-Dunford-Pettis sets in Banach lattices and its applications

Pages : 599-607

View : 47 | Download : 11

Publication Date : 2020-04-02

Article Type : Research Paper

Abstract :We introduce and study the notion of almost L-Dunford-Pettis sets in Banach lattices and we give some characterizations of it in terms of sequences. As an application, we establish new properties of almost Dunford-Pettis completely continuous operators. Finally, by introducing the concept of aL-Dunford-Pettis property in Banach lattices, we investigate the weak compactness of almost Dunford-Pettis completely continuous operator.
Keywords : Banach lattice, Dunford Pettis set, relatively compact Dunford Pettis property, Dunford Pettis completely continuous operator

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