Order bounded operators and tensor products of Banach lattices.
N.J. Nielsen, S. Heinrich (1981)
Mathematica Scandinavica
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N.J. Nielsen, S. Heinrich (1981)
Mathematica Scandinavica
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Nielsen, N. J.
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D.H. Fremlin (1974)
Mathematische Annalen
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Arno Jaeger, Yueh-er Kuo (1966)
Monatshefte für Mathematik
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Jörg Eschmeier (1988)
Journal für die reine und angewandte Mathematik
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Ju. A. Abramovič, L. P. Janovskiĭ (1982)
Colloquium Mathematicae
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Dirk Werner (1987)
Mathematica Scandinavica
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W.E. Fitzgibbon (1977)
Monatshefte für Mathematik
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Ray Redheffer, Wolfgang Walter (1986)
Monatshefte für Mathematik
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N. J. Nielsen (1980-1981)
Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
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Julio Flores, César Ruiz (2006)
Studia Mathematica
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Given a positive Banach-Saks operator T between two Banach lattices E and F, we give sufficient conditions on E and F in order to ensure that every positive operator dominated by T is Banach-Saks. A counterexample is also given when these conditions are dropped. Moreover, we deduce a characterization of the Banach-Saks property in Banach lattices in terms of disjointness.
Julio Flores, Pedro Tradacete (2008)
Studia Mathematica
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It is proved that every positive Banach-Saks operator T: E → F between Banach lattices E and F factors through a Banach lattice with the Banach-Saks property, provided that F has order continuous norm. By means of an example we show that this order continuity condition cannot be removed. In addition, some domination results, in the Dodds-Fremlin sense, are obtained for the class of Banach-Saks operators.