Banach Lattices with the Positive Dunford-Pettis Relatively Compact Property
DOI:
https://doi.org/10.17398/Keywords:
positive Dunford-Pettis relatively compact property, almost Dunford-Pettis completely continuous operator, almost Dunford-Pettis set, Banach latticeAbstract
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.
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