Article

Positivity

, Volume 17, Issue 3, pp 759-773

Open Access This content is freely available online to anyone, anywhere at any time.

On the dual positive Schur property in Banach lattices

  • Witold WnukAffiliated withFaculty of Mathematics and Computer Science, A. Mickiewicz University Email author 

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.

Keywords

Schur property Positive Schur property Grothendieck property Positive Grothendieck property

Mathematics Subject Classification (2000)

46B42 47B65 46B45 46E30