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

Year 2020, Volume: 49 Issue: 2, 599 - 607, 02.04.2020

Abderrahman Retbı

https://doi.org/10.15672/hujms.568386

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

References

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