Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Removable sets of support points of convex sets in Banach spaces
HTML articles powered by AMS MathViewer

by R. R. Phelps PDF
Proc. Amer. Math. Soc. 99 (1987), 319-322 Request permission


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.
  • 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
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46B20, 47D07, 52A07
  • Retrieve articles in all journals with MSC: 46B20, 47D07, 52A07
Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 99 (1987), 319-322
  • MSC: Primary 46B20; Secondary 47D07, 52A07
  • DOI:
  • MathSciNet review: 870793