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Proceedings of the American Mathematical Society

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



Extreme points in function spaces

Author: Dirk Werner
Journal: Proc. Amer. Math. Soc. 89 (1983), 598-600
MSC: Primary 46E40; Secondary 47D15
MathSciNet review: 718980
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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.

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Keywords: Extreme point, spaces of vector-valued functions, nice operator, spaces of compact operators
Article copyright: © Copyright 1983 American Mathematical Society

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