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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E. Asplund,Fréchet differentiability of convex functions, Acta Math.121 (1968), 31–47.
E. Asplund,Boundedly Krein-compact Banach spaces, Proceedings of the Functional Analysis Week, Aarhus, 1969, pp. 1–4.
E. Asplund, and R. T. Rockafellar,Gradients of convex functions, Trans. Amer. Math. Soc.139 (1969), 344–467.
C. Bessaga, and A. Pełczyński,On extreme points in separable conjugate spaces, Israel J. Math.4 (1966), 252–264.
S. L. Troyanski,On locally uniformly convex and differentiable norms in certain non-separable Banach spaces, Studia Math.37 (1971), 173–180.
Author information
Authors and Affiliations
Additional information
This research was supported by the National Research Council of Canada, Grant A-3999.
Rights and permissions
About this article
Cite this article
Collier, J., Edelstein, M. On strongly exposed points and frechet differentiability. Israel J. Math. 17, 66–68 (1974). https://doi.org/10.1007/BF02756826
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02756826