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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.

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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