Banach lattices with the positive Dunford-Pettis relatively compact property

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Banach lattices with the positive Dunford-Pettis relatively compact property

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Title: Banach lattices with the positive Dunford-Pettis relatively compact property
Author: El Fahri, K.; Machrafi, N.; Moussa, M.
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
Date: 2015


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