Israel Journal of Mathematics

, Volume 17, Issue 1, pp 66–68 | Cite as

On strongly exposed points and frechet differentiability

  • J. Collier
  • M. Edelstein
Article
Received:

Abstract

Using properties of convex functionals, it is shown that closed and bounded convex sets in a class of Banach spaces which includes separable conjugate spaces are the closed convex hulls of their strongly exposed points.

Keywords

Banach Space Convex Function Convex Hull Convex Subset Reflexive Banach Space 
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.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E. Asplund,Fréchet differentiability of convex functions, Acta Math.121 (1968), 31–47.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    E. Asplund,Boundedly Krein-compact Banach spaces, Proceedings of the Functional Analysis Week, Aarhus, 1969, pp. 1–4.Google Scholar
  3. 3.
    E. Asplund, and R. T. Rockafellar,Gradients of convex functions, Trans. Amer. Math. Soc.139 (1969), 344–467.CrossRefMathSciNetGoogle Scholar
  4. 4.
    C. Bessaga, and A. Pełczyński,On extreme points in separable conjugate spaces, Israel J. Math.4 (1966), 252–264.Google Scholar
  5. 5.
    S. L. Troyanski,On locally uniformly convex and differentiable norms in certain non-separable Banach spaces, Studia Math.37 (1971), 173–180.MATHMathSciNetGoogle Scholar

Copyright information

© Hebrew University 1974

Authors and Affiliations

  • J. Collier
    • 1
  • M. Edelstein
    • 1
  1. 1.Department of MathematicsDalhousie UniversityHalifaxCanada

Personalised recommendations