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
Part of the Lecture Notes in Mathematics book series (LNM, volume 1166)


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.


Banach Space Probability Measure Extreme Point Tree Index Springer Lecture Note 
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    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
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    A. Ho: The Krein-Milman property and complemented bushes in Banach space, Pac. J. of Math. 98 (1982), p. 347–363.CrossRefzbMATHGoogle Scholar
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    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
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    J. Lindenstrauss, L. Tzafriri: Classical Banach spaces, vol. 1, Springer 1977.Google Scholar
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    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
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    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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