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Sur les opérateurs de Dunford–Pettis positifs qui sont faiblement compacts. (On weakly compact positive Dunford–Pettis operators.) (English) Zbl 1099.46016
The authors give necessary and sufficient conditions concerning the Dunford–Pettis property. They establish the following Theorem. Let $$E$$ be a Banach lattice. Then every positive Dunford–Pettis operator from $$E$$ into $$E$$ is weakly compact if and only if for every positive Dunford–Pettis operator $$T:E\to E$$, $$T^2$$ is compact. Some other equivalences are given.

##### MSC:
 46B42 Banach lattices 47B07 Linear operators defined by compactness properties
##### Keywords:
Dunford-Pettis property; Dunford-Pettis operator
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##### References:
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