On the Dunford-Pettis property
Bombal, Fernando (1988)
Portugaliae mathematica
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Bombal, Fernando (1988)
Portugaliae mathematica
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Ioana Ghenciu, Paul Lewis (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
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Dunford-Pettis type properties are studied in individual Banach spaces as well as in spaces of operators. Bibasic sequences are used to characterize Banach spaces which fail to have the Dunford-Pettis property. The question of whether a space of operators has a Dunford-Pettis property when the dual of the domain and the codomain have the respective property is studied. The notion of an almost weakly compact operator plays a consistent and important role in this study.
Belmesnaoui Aqzzouz, Aziz Elbour, Othman Aboutafail (2011)
Commentationes Mathematicae Universitatis Carolinae
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We characterize Banach lattices on which every positive almost Dunford-Pettis operator is weakly compact.
Jesús M. Fernández Castillo, Fernando Sánchez (1993)
Revista Matemática de la Universidad Complutense de Madrid
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Diómedes Bárcenas (1991)
Extracta Mathematicae
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Belmesnaoui Aqzzouz, Aziz Elbour, Mohammed Moussa (2012)
Mathematica Bohemica
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We establish some sufficient conditions under which the subspaces of Dunford-Pettis operators, of M-weakly compact operators, of L-weakly compact operators, of weakly compact operators, of semi-compact operators and of compact operators coincide and we give some consequences.
Ioana Ghenciu, Paul Lewis (2006)
Colloquium Mathematicae
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The Dunford-Pettis property and the Gelfand-Phillips property are studied in the context of spaces of operators. The idea of L-sets is used to give a dual characterization of the Dunford-Pettis property.
Jesús M. Fernández Castillo (1990)
Extracta Mathematicae
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In this note we review some results about: 1. Representation of Absolutely (∞,p) summing operators (∏∞,p) in C(K,E) 2. Dunford-Pettis properties.