, Volume 37, Issue 1-2, pp 34-47

Dunford-pettis operators onL 1 and the Radon-Nikodym property

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Abstract

Using the duality between Dunford-Pettis operators onL 1 and Pettis-Cauchy martingales, we prove that the Dunford-Pettis operators fromL 1 intoL 1 form a lattice. We show also that a Banach spaceX has the Radon-Nikodým property provided the Dunford-Pettis members of ℒ(L 1,X) are representable. The lifting of dual valued Dunford-Pettis operators is investigated. Some remarks are included.