# On the dual positive Schur property in Banach lattices

On the dual positive Schur property in Banach lattices 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# On the dual positive Schur property in Banach lattices

, Volume 17 (3) – Sep 16, 2012
15 pages

/lp/springer_journal/on-the-dual-positive-schur-property-in-banach-lattices-jKN2tX0Hr3
Publisher
Springer Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-012-0203-7
Publisher site
See Article on Publisher Site

### 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.

### Journal

PositivitySpringer Journals

Published: Sep 16, 2012

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