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

Yıl 2020, Cilt: 49 Sayı: 2, 599 - 607, 02.04.2020

Abderrahman Retbı

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

Öz

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.

Anahtar Kelimeler

Banach lattice, Dunford-Pettis set, relatively compact Dunford-Pettis property, Dunford-Pettis completely continuous operator

Kaynakça

• [1] C.D. Aliprantis and O. Burkinshaw, Positive operators, Reprint of the 1985 original. Springer, Dordrecht, 2006.
• [2] K.T. Andrews, Dunford-Pettis sets in the space of Bochner integrable functions, Math. Ann. 241, 35-41, 1979.
• [3] K. Bouras, Almost Dunford-Pettis sets in Banach lattices, Rend. Circ. Mat. Palermo. 62, 227-236, 2013.
• [4] K. El Fahri, N. Machrafi and M. Moussa, Banach Lattices with the Positive Dunford- Pettis Relatively Compact Property, Extracta Math. 30 (2), 161-179, 2015.
• [5] P. Meyer-Nieberg, Banach lattices, Universitext, Springer-Verlag, Berlin, 1991.
• [6] A. Retbi and B. El Wahbi, L-Dunford-Pettis property in Banach spaces, Methods Funct. Anal. Topology, accepted.
• [7] Y. Wen and J. Chen, Characterizations of Banach Spaces With Relatively Compact Dunford-Pettis Sets, Advances in Mathematics (China), 45 (1), 122-132, 2016.