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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.
Appears in Collections:Extracta Mathematicae Vol. 30, nº 2 (2015)

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