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  • Currently known as: Journal of the Australian Mathematical Society Title history
    Journal of the Australian Mathematical Society, Volume 73, Issue 2
  • October 2002, pp. 251-278

The Schur and (weak) Dunford-Pettis properties in Banach lattices

  • Anna Kamińska (a1) and Mieczysław Mastyło (a2)
  • DOI: http://dx.doi.org/10.1017/S144678870000882X
  • Published online: 01 April 2009
Abstract
Abstract

We 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.

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