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http://hdl.handle.net/10662/9022
| Title: | Banach lattices with the positive Dunford-Pettis relatively compact property |
| Authors: | El Fahri, K. Machrafi, N. Moussa, M. |
| Keywords: | The positive Dunford-Pettis relatively compact property;Almost Dunford-Pettis completely continuous operator;Almost Dunford-Pettis set;Banach lattice;Propiedad relativamente compacta positiva de Dunford-Pettis;Conjunto de casi todo Dunford-Pettis;Enrejado de Banach;Operador casi continuo de casi todo el sistema de Dunford-Pettis |
| Issue Date: | 2015 |
| Publisher: | Universidad de Extremadura |
| Abstract: | The paper is devoted to such Banach lattices E that every Dunford-Pettis and weakly null sequence (x_n) ⊂ E with disjoint terms is norm null (the positive Dunford-Pettis relatively compact property). It is established that a Banach lattice E has the positive Dunford-Pettis relatively compact property if and only if its almost Dunford-Pettis subsets are L-weakly compact. Consequently, we derive the following result: Banach lattices with the property that their almost Dunford-Pettis subsets are relatively compact, are precisely the discrete KB-spaces. |
| URI: | http://hdl.handle.net/10662/9022 |
| Appears in Collections: | Extracta Mathematicae Vol. 30, nº 2 (2015) |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| 2605-5686_30_2_161.pdf | 127,83 kB | Adobe PDF | View/Open |
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