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.
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Bourgain, J. Dunford-pettis operators onL 1 and the Radon-Nikodym property. Israel J. Math. 37, 34–47 (1980). https://doi.org/10.1007/BF02762866
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DOI: https://doi.org/10.1007/BF02762866