Extreme points in function spaces

Werner, Dirk

doi:10.1090/S0002-9939-1983-0718980-3

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.

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