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Banach lattices with the weak Dunford-Pettis property. (English) Zbl 0805.46023
Summary: The paper is devoted to such Banach lattices $$E$$ that every weakly compact operator from $$E$$ into a Banach space maps weakly null sequences with disjoint terms onto norm null sequences (the weak Dunford-Pettis property). Moreover, we investigate relations between the positive Schur property and the weak Dunford-Pettis property. We notice also that the weak Dunford-Pettis property is inherited by closed ideals.

##### MSC:
 46B42 Banach lattices 46B22 Radon-Nikodým, Kreĭn-Milman and related properties