- Hacettepe Journal of Mathematics and Statistics
- Vol: 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
Authors : Abderrahman Retbi
Pages : 599-607
Doi:10.15672/hujms.568386
View : 10 | Download : 5
Publication Date : 2020-04-02
Article Type : Research
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