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

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

Abderrahman Retbi
Sayfa
599–607
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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 Maddede Bu Makale

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Amaç & Hipotez: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.
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Temel Bulgular & Veri:As an application, we establish new properties of almost Dunford-Pettis completely continuous operators.
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Sonuç & Katkı: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.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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.

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Bu Makaleye Atıf Yap

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

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Kaynakça (7)

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  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.