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Representations of Orlicz lattices

Witold Wnuk — 1984

CONTENTSIntroduction................................................................................................................................5Preliminaries..............................................................................................................................5  A. Vector lattices......................................................................................................................6  B. Measure theory.................................................................................................................12Musielak-Orlicz...

Some characterizations of Banach lattices with the Schur property.

Witold Wnuk — 1989

Revista Matemática de la Universidad Complutense de Madrid

This note contains a short proof of the equivalence of the Schur and Dunford-Pettis properties in the class of discrete KB-spaces. We also present an operator characterization of the Schur property (Theorem 2) and we notice that Banach lattices which band hereditary l1 coincide with Banach lattices having the Schur property. (This characterization is due to Popa (1977)). Moreover, the paper offers examples of Banach lattices with the positive Schur property and without the Schur property and which...

Copies of in F-lattices

Witold Wnuk — 2016

Commentationes Mathematicae

Modifying ideas presented in [14] we prove that a complete metrizable locally solid Riesz space E contains a linear subspace linearly homeomorphic to iff E contains a sublattice order isomorphic to .

On the modulus of measures with values in topological Riesz spaces.

Lech DrewnowskiWitold Wnuk — 2002

Revista Matemática Complutense

The paper is devoted to a study of some aspects of the theory of (topological) Riesz space valued measures. The main topics considered are the following. First, the problem of existence (and, particularly, the so-called proper existence) of the modulus of an order bounded measure, and its relation to a similar problem for the induced integral operator. Second, the question of how properties of such a measure like countable additivity, exhaustivity or so-called absolute exhaustivity, or the properties...

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