Dunford-pettis operators onL1 and the Radon-Nikodym property
Using the duality between Dunford-Pettis operators onL1 and Pettis-Cauchy martingales, we prove that the Dunford-Pettis operators fromL1 intoL1 form a lattice. We show also that a Banach spaceX has the Radon-Nikodým property provided the Dunford-Pettis members of ℒ(L1,X) are representable. The lifting of dual valued Dunford-Pettis operators is investigated. Some remarks are included.
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