SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 2

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

Abderrahman Retbi
Pages
599–607
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
📊
Key Findings & Data:As an application, we establish new properties of almost Dunford-Pettis completely continuous operators.
💡
Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Banach lattice · Dunford-Pettis set · relatively compact Dunford-Pettis property

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.

🔖

Cite This Article

Retbi, A. (2022). Almost L-Dunford-Pettis sets in Banach lattices and its applications. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 2, 599–607. https://ajindex.com/articles/529611

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (7)

  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.