, Volume 17, Issue 3, pp 759-773,
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On the dual positive Schur property in Banach lattices

Abstract

The paper contains several characterizations of Banach lattices $E$ with the dual positive Schur property (i.e., $0 \le f_n \xrightarrow {\sigma (E^*,E)} 0$ implies $\Vert f_n\Vert \rightarrow 0$ ) and various examples of spaces having this property. We also investigate relationships between the dual positive Schur property, the positive Schur property, the positive Grothendieck property and the weak Dunford–Pettis property.

This research was partially supported by The National Center of Science, Poland, Grant no. N N 201 605340.