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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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Extreme points in function spaces
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by Dirk Werner PDF
Proc. Amer. Math. Soc. 89 (1983), 598-600 Request permission

Abstract:

We show that the extreme points of the unit ball of $C(K,{L^1}(\mu ))$ ($K$ compact Hausdorff, $(\Omega ,\Sigma ,\mu )$ arbitrary) are precisely the functions with extremal values. The result is applied to characterize the extreme points of the unit ball of certain spaces of compact operators.
References
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 89 (1983), 598-600
  • MSC: Primary 46E40; Secondary 47D15
  • DOI: https://doi.org/10.1090/S0002-9939-1983-0718980-3
  • MathSciNet review: 718980