Israel Journal of Mathematics

, Volume 37, Issue 1, pp 34–47

Dunford-pettis operators onL1 and the Radon-Nikodym property

  • J. Bourgain

DOI: 10.1007/BF02762866

Cite this article as:
Bourgain, J. Israel J. Math. (1980) 37: 34. doi:10.1007/BF02762866


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.

Copyright information

© The Weizmann Science Press of Israel 1980

Authors and Affiliations

  • J. Bourgain
    • 1
  1. 1.Vrije Universiteit BrusselBrusselsBelgium