Dunford-pettis operators onL 1 and the Radon-Nikodym property
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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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- 1.J. Bourgain,Sets with the Radon-Nikodým property in conjugate Banach spaces, Studia Math.663 (1978).Google Scholar
- 2.J. Bourgain,A non-dentable set without the tree-property, Studia Math.682 (1980), to appear.Google Scholar
- 4.J. Diestel,Topics in Geometry of Banach Spaces, No. 485, Springer Verlag, 1975.Google Scholar
- 5.J. Diestel and J. J. Uhl,The Theory of Vector Measures, Mathematical Surveys, Vol. 15, Amer. Math. Soc., 1977.Google Scholar
- 6.K. Musial,The weak Radon-Nikodým property in Banach spaces, to appear.Google Scholar
- 7.H. Rosenthal,Convolution by a biased coin, The Altgeld Book 1975/76, University of Illinois, Functional Analysis Seminar.Google Scholar