On Banach ideals determined by Banach lattices and their applications

N. J. Nielsen

Displaying similar documents to “On Banach ideals determined by Banach lattices and their applications”

Application of Rademacher systems to operator characterizations of Banach lattices

Ju. A. Abramovič, L. P. Janovskiĭ (1982)

Colloquium Mathematicae

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Domination by positive Banach-Saks operators

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.

Factorization and domination of positive Banach-Saks operators

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.

The Hahn-Banach Theorem surveyed

Gerard Buskes

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CONTENTS1. Prerequisites....................................................................................52. The history.......................................................................................63. Helly's Part.......................................................................................64. Banach's proof.................................................................................75. The shortest proof...........................................................................86....