Banach lattices with the positive Dunford-Pettis relatively compact property

• Kamal El Fahri ^[1] ; Nabil Machrafi ^[1] ; Mohammed Moussa ^[1]
  1. [1] Université Ibn-Tofail

     Université Ibn-Tofail

     Kenitra, Marruecos

     
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 30, Nº 2, 2015, págs. 161-179
• Idioma: inglés
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• Resumen

  • The paper is devoted to such Banach lattices E that every Dunford-Pettis and weakly null sequence (xn)  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.