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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Removable sets of support points of convex sets in Banach spaces
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by R. R. Phelps PDF
Proc. Amer. Math. Soc. 99 (1987), 319-322 Request permission

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
  • Errett Bishop and R. R. Phelps, The support functionals of a convex set, Proc. Sympos. Pure Math., Vol. VII, Amer. Math. Soc., Providence, R.I., 1963, pp. 27–35. MR 0154092
  • H. N. Bojadziev, Characterization of the generators of $C_{0}$ semigroups which leave a convex set invariant, Comment. Math. Univ. Carolin. 25 (1984), no. 1, 159–170. MR 749124
  • Arne Brøndsted, On a lemma of Bishop and Phelps, Pacific J. Math. 55 (1974), 335–341. MR 380343
  • Josef Daneš, A geometric theorem useful in nonlinear functional analysis, Boll. Un. Mat. Ital. (4) 6 (1972), 369–375 (English, with Italian summary). MR 0317130
  • Robert H. Martin Jr., Invariant sets for evolution systems, International Conference on Differential Equations (Proc., Univ. Southern California, Los Angeles, Calif., 1974) Academic Press, New York, 1975, pp. 510–536. MR 0467042
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 99 (1987), 319-322
  • MSC: Primary 46B20; Secondary 47D07, 52A07
  • DOI: https://doi.org/10.1090/S0002-9939-1987-0870793-1
  • MathSciNet review: 870793