Author:
Kamińska Anna,Mastyło Mieczysław
Abstract
AbstractWe study the Schur and (weak) Dunford-Pettis properties in Banach lattices. We show that l1, c0 and l∞ are the only Banach symmetric sequence spaces with the weak Dunford-Pettis property. We also characterize a large class of Banach lattices without the (weak) Dunford-Pettis property. In MusielakOrlicz sequence spaces we give some necessary and sufficient conditions for the Schur property, extending the Yamamuro result. We also present a number of results on the Schur property in weighted Orlicz sequence spaces, and, in particular, we find a complete characterization of this property for weights belonging to class ∧. We also present examples of weighted Orlicz spaces with the Schur property which are not L1-spaces. Finally, as an application of the results in sequence spaces, we provide a description of the weak Dunford-Pettis and the positive Schur properties in Orlicz spaces over an infinite non-atomic measure space.
Publisher
Cambridge University Press (CUP)
Reference36 articles.
1. Modulared sequence spaces;Yamamuro;J. Fac. Sci. Hokkaido Univ. Ser. I.,1954
2. On modular sequence spaces
3. Banach lattices with the weak Dunford-Pettis property;Wnuk;Atti Sem. Mat. Fis. Univ. Modena,1994
4. Banach lattices with properties of the Schur type—a survey;Wnuk;Confer Sem. Mar. Univ. Bari,1993
5. Onl p -copies in Musielak-Orlicz sequence spaces
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