Application of Rademacher systems to operator characterizations of Banach lattices
Ju. A. Abramovič, L. P. Janovskiĭ (1982)
Colloquium Mathematicae
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Ju. A. Abramovič, L. P. Janovskiĭ (1982)
Colloquium Mathematicae
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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.
Gerard Buskes
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CONTENTS1. Prerequisites....................................................................................52. The history.......................................................................................63. Helly's Part.......................................................................................64. Banach's proof.................................................................................75. The shortest proof...........................................................................86....
William Feldmann (1988)
Mathematische Zeitschrift
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O. Reynov (1981)
Studia Mathematica
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C.D. Aliprantis, Owen Burkinshaw (1980)
Mathematische Zeitschrift
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N. Ghoussoub, W.B. Johnson (1987)
Mathematische Zeitschrift
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H. G. Dales, Tomasz Kania, Tomasz Kochanek, Piotr Koszmider, Niels Jakob Laustsen (2013)
Studia Mathematica
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Antonio S. Granero, Mar Jiménez, Alejandro Montesinos, José P. Moreno, Anatolij Plichko (2003)
Studia Mathematica
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Richard Haydon (1977)
Mathematische Zeitschrift
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Radu Zaharopol (1986)
Mathematische Zeitschrift
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F. Oertel (1996)
Acta Universitatis Carolinae. Mathematica et Physica
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