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On the radon-nikodym property in function spaces

  • N. Ghoussoub
  • B. Maurey
Conference paper
  • 290 Downloads
Part of the Lecture Notes in Mathematics book series (LNM, volume 1166)

Abstract

Using the topological methods introduced in [3], we give a simple proof of a theorem of Talagrand [7] which asserts that Banach lattices with the Radon-Nikodym property are isometric to dual Banach lattices. We also give a proof of a recent result announced by Diestel

Keywords

Banach Lattice Continuity Property Order Ideal Lattice Homomorphism Measurable Random Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    J. Bourgain, H.P. Rosenthal: "Geometrical implications of certain finite dimensional decompositions". Bull. Soc. Math. Belg. 32 p.57–82 (1980).MathSciNetzbMATHGoogle Scholar
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    N. Ghoussoub, B. Maurey: "Hδ-embeddings in Hilbert space and optimization on Gδ-sets", to appear in Memoirs of the A.M.S (1985)Google Scholar
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    Y. Lindenstrauss, L. Tzafriri: "Classical Banach spaces. II. Function spaces, Springer-Verlag 97 (1979).Google Scholar
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    H.P. Lotz: "Extensions and liftings of positive linear operators", T.A.M.S. 211, p. 85–100 (1975).MathSciNetCrossRefzbMATHGoogle Scholar
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    M. Talagrand: "La structure des spaces de Banach reticules ayant la propriete de Radon-Nikodym", Israel J. Math. 44 No. 3, (1983).Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • N. Ghoussoub
    • 1
  • B. Maurey
    • 2
  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.Université Paris VIIParisFrance

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