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Proceedings of the American Mathematical Society

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



Decomposable compact convex sets and peak sets for function spaces.

Author: Leonard Asimow
Journal: Proc. Amer. Math. Soc. 25 (1970), 75-79
MSC: Primary 46.55
MathSciNet review: 0259607
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Abstract: Geometric conditions are known under which a closed face of a compact convex set is a peak set with respect to the space of continuous affine (real-valued) functions. The purpose of this note is to give an application of this “abstract-geometric” set-up to the problem of finding peak sets (or points) in a compact Hausdorff space with respect to a closed subspace of continuous complex-valued functions. In this fashion we obtain the strong hull criteria of Curtis and Figá-Talamanca and in particular the Bishop peak point theorem for function algebras.

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Keywords: Compact convex sets, Functions spaces, affine functions, extreme points, functions algebras, peak sets, peak faces, strong hull
Article copyright: © Copyright 1970 American Mathematical Society