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Strongly exposed points in weakly compact convex sets in Banach spaces


Author: J. Bourgain
Journal: Proc. Amer. Math. Soc. 58 (1976), 197-200
MSC: Primary 46B05
DOI: https://doi.org/10.1090/S0002-9939-1976-0415272-3
MathSciNet review: 0415272
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Abstract: A ``purely geometric'' proof of the Lindenstrauss-Troyanski result ([2], [6]) on strongly exposed points of weakly compact sets in Banach spaces is given.

I would like to thank the referee for his suggestions.


References [Enhancements On Off] (What's this?)

  • [1] E. Bishop and R. R. Phelps, The support functionals of a convex set, Proc. Sympos. Pure Math., vol. 7, Amer. Math. Soc., Providence, R.I., 1963, pp. 27-35. MR 27 #4051. MR 0154092 (27:4051)
  • [2] J. Lindenstrauss, On operators which attain their norm, Israel J. Math. 1 (1963), 139-148. MR 28 #3308. MR 0160094 (28:3308)
  • [3] I. Namioka, Neighbourhoods of extreme points, Israel J. Math. 5 (1967), 145-152. MR 36 #4323. MR 0221271 (36:4323)
  • [4] R. R. Phelps, Dentability and extreme points in Banach spaces, J. Functional Analysis 17 (1974), 78-90. MR 50 #5427. MR 0352941 (50:5427)
  • [5] -, Lectures on Choquet's theorem, Van Nostrand, Princeton, N.J., 1966. MR 33 #1690.
  • [6] S. L. Trojanski, On locally uniformly convex and differentiable norms in certain non-separable Banach spaces, Studia Math. 37 (1970/71), 173-180. MR 46 #5995. MR 0306873 (46:5995)

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DOI: https://doi.org/10.1090/S0002-9939-1976-0415272-3
Article copyright: © Copyright 1976 American Mathematical Society

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