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On a theorem of J. Bourgain on finite dimensional decompositions and the radon-nikodym property

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1267)

Abstract

We give an exposition of the “hard case” of Bourgain's theorem, that a Banach space X has RNP iff each subspace with a finite dimensional decomposition has RNP. We reproduce essentially Bourgain's arguments, by explaining the ideas underlying the proof and giving slightly altered arguments for some of the technical details.

Keywords

  • Banach Space
  • Unit Sphere
  • Finite Subset
  • Finite Dimensional Subspace
  • Martingale Difference

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© 1987 Springer-Verlag

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Schachermayer, W. (1987). On a theorem of J. Bourgain on finite dimensional decompositions and the radon-nikodym property. In: Lindenstrauss, J., Milman, V.D. (eds) Geometrical Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 1267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078139

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  • DOI: https://doi.org/10.1007/BFb0078139

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18103-3

  • Online ISBN: 978-3-540-47771-6

  • eBook Packages: Springer Book Archive