On the dual positive Schur property in Banach lattices
By W. Wnuk. 2013
75 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/021976ea130366b4e4966bcab54371f044dab4d8
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In Applied Mathematics
In Mathematical Physics
Citations in the corpus
- Unbounded norm topology in Banach lattices (2016, background): “Propositions 4.3, 4.4, and 4.6 in [Gao14] remain valid under the additional assumption thatX∗ is order continuous (note that the dual positive Schur property already implies that X∗ is order continuous by [Wnuk13, Proposition 2.1]).”