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Removable sets of support points of convex sets in Banach spaces

Author: R. R. Phelps
Journal: Proc. Amer. Math. Soc. 99 (1987), 319-322
MSC: Primary 46B20; Secondary 47D07, 52A07
MathSciNet review: 870793
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Abstract: A corollary of the Bishop-Phelps theorem is that a closed convex subset $ C$ of a Banach space can always be represented as the intersection of its supporting closed half-spaces. In this paper an investigation is made of those subsets $ S$ of $ C$ such that $ C$ is the intersection of those closed half-spaces which support it at points of $ C\backslash S$. This will be true for sets $ S$ which are "small" relative to $ C$, where smallness can be measured in terms of dimension, density character, or $ \sigma $-compactness.

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

  • [1] Errett 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 0154092 (27:4051)
  • [2] K. N. Boyadzhiev, Characterization of the generators of $ {C_0}$ semigroups which leave a convex set invariant, Comment. Math. Univ. Carolinae 25 (1984), 159-170. MR 749124 (85k:47079)
  • [3] A. Brøndsted, On a lemma of Bishop and Phelps, Pacific J. Math. 55 (1974), 335-341. MR 0380343 (52:1243)
  • [4] J. Danes, A geometric theorem useful in nonlinear functional analysis, Boll. Un. Mat. Ital. (4) 6 (1972), 369-375. MR 0317130 (47:5678)
  • [5] R. Martin, Invariant sets for evolution systems, International Conf. on Diff. Equations, Academic Press, New York, 1975. MR 0467042 (57:6911)

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Keywords: Convex sets, Banach spaces, support points
Article copyright: © Copyright 1987 American Mathematical Society

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