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A note on the positive Schur property. (English) Zbl 0694.46020
The author proves that for a Banach lattice \((E,\| \cdot \|)\) the following statements are equivalent:
(i) E is \(\sigma\)-Dedekind complete and any operator T: \(E\to C_ 0\) is a Dunford-Pettis operator iff T is regular;
(ii) E has the positive Schur property, i.e. \((x_ n)\subset E_+\) and \(x_ n\to 0\) weakly imply \(\| x_ n\| \to 0\).
Reviewer: S.S.Kutateladze

46B42 Banach lattices
47B60 Linear operators on ordered spaces
Full Text: DOI
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