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On the radon-nikodym property in function spaces

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

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References

  1. J. Bourgain, H.P. Rosenthal: "Geometrical implications of certain finite dimensional decompositions". Bull. Soc. Math. Belg. 32 p.57–82 (1980).

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  2. J. Diestel: Personal communication (1983).

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  3. N. Ghoussoub, B. Maurey: "Gδ-embeddings in Hilbert space", Journal of Funct. Analysis Vol 61, No. 1, p. 72–97 (1985)

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  4. N. Ghoussoub, B. Maurey: "Hδ-embeddings in Hilbert space and optimization on Gδ-sets", to appear in Memoirs of the A.M.S (1985)

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  5. Y. Lindenstrauss, L. Tzafriri: "Classical Banach spaces. II. Function spaces, Springer-Verlag 97 (1979).

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  6. H.P. Lotz: "Extensions and liftings of positive linear operators", T.A.M.S. 211, p. 85–100 (1975).

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  7. M. Talagrand: "La structure des spaces de Banach reticules ayant la propriete de Radon-Nikodym", Israel J. Math. 44 No. 3, (1983).

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© 1985 Springer-Verlag

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Ghoussoub, N., Maurey, B. (1985). On the radon-nikodym property in function spaces. In: Kalton, N.J., Saab, E. (eds) Banach Spaces. Lecture Notes in Mathematics, vol 1166. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074693

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  • DOI: https://doi.org/10.1007/BFb0074693

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16051-9

  • Online ISBN: 978-3-540-39736-6

  • eBook Packages: Springer Book Archive