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

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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

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References

  1. 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.

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  2. A. Ho: The Krein-Milman property and complemented bushes in Banach space, Pac. J. of Math. 98 (1982), p. 347–363.

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  3. 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.

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  4. J. Lindenstrauss, L. Tzafriri: Classical Banach spaces, vol. 1, Springer 1977.

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  5. 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).

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  6. 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).

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© 1985 Springer-Verlag

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Schachermayer, W. (1985). Some remarks concerning the krein-milman and the radon-nikodym property of Banach spaces. In: Kalton, N.J., Saab, E. (eds) Banach Spaces. Lecture Notes in Mathematics, vol 1166. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074704

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  • DOI: https://doi.org/10.1007/BFb0074704

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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