CONTENTSIntroduction................................................................................................................................5Preliminaries..............................................................................................................................5 A. Vector lattices......................................................................................................................6 B. Measure theory.................................................................................................................12Musielak-Orlicz...
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...
Modifying ideas presented in [14] we prove that a complete metrizable locally solid Riesz space contains a linear subspace linearly homeomorphic to iff contains a sublattice order isomorphic to .
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...
We describe, using elementary methods, the Köthe dual of variable Lebesgue spaces called also Nakano spaces, independenly for and . The case when is also included.
We investigate relationships joining the order continuity of a norm in a Banach lattice and some composition properties of L-weakly and M-weakly compact operators. Our results improve Proposition 3.6.16 from [5].
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