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

DOI:
https://doi.org/10.1090/S0002-9939-1987-0870793-1

MathSciNet review:
870793

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Abstract: A corollary of the Bishop-Phelps theorem is that a closed convex subset 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 of such that is the intersection of those closed half-spaces which support it at points of . This will be true for sets which are "small" relative to , where smallness can be measured in terms of dimension, density character, or -compactness.

**[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**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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1987-0870793-1

Keywords:
Convex sets,
Banach spaces,
support points

Article copyright:
© Copyright 1987
American Mathematical Society