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Banach Spaces pp 169-176 | Cite as

Some remarks concerning the krein-milman and the radon-nikodym property of Banach spaces

  • W. Schachermayer
Conference paper
  • 298 Downloads
Part of the Lecture Notes in Mathematics book series (LNM, volume 1166)

Abstract

We present an example, simplifying an earlier one due to R. C. James, of a l-separated tree with empty wedge intersections such that its closed convex hull has continuum many extreme points.

Keywords

Banach Space Probability Measure Extreme Point Tree Index Springer Lecture Note 
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

  1. [B-T]
    J. Bourgain, M. Talagrand: Dans un espace de Banach réticulé solide, la propriété de Radon-Kikodym et celle de Krein-Milman sont equivalent. Proc. AMS 81 (1981), p. 93–96.MathSciNetzbMATHGoogle Scholar
  2. [H]
    A. Ho: The Krein-Milman property and complemented bushes in Banach space, Pac. J. of Math. 98 (1982), p. 347–363.CrossRefzbMATHGoogle Scholar
  3. [J]
    R.C. James: Extreme points and an unusual Banach space, appeared in Banach space theory and its applications, Springer lecture notes 991 (1983), p. 111–123.Google Scholar
  4. [J-T]
    J. Lindenstrauss, L. Tzafriri: Classical Banach spaces, vol. 1, Springer 1977.Google Scholar
  5. [S]
    W. Schachermayer: For a Banach space isomorphic to its square the Radon-Nikodym property and the Krein-Milman property are equivalent, to appear in Studia Math. (1985).Google Scholar
  6. [ST]
    C. Stegall: The Radon-Nikodym property in Banach spaces, Part I, appeared in "Vorlesungen uas dem FB. Mathematik der Universität Essen, Heft 10, Essen (1983).Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • W. Schachermayer
    • 1
  1. 1.Department of MathematicsUniversitat LinzLinzAustria

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