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Extreme points in \(C(K,L^{\phi}(\mu))\). (English) Zbl 0606.46019

Let \(L^{\phi}(\mu)\) denote an Orlicz space and let \(\phi\) satisfy the condition \(\Delta_ 2\). It is shown that the extreme points of the unit ball of the space of continuous functions from a compact Hausdorff space K into \(L^{\phi}(\mu)\) with supremum norm on \(C(K,L^{\phi}(\mu))\) are precisely the functions with values in the set of extreme points of the unit ball of \(L^{\phi}(\mu)\).

MSC:

46E40 Spaces of vector- and operator-valued functions
46B20 Geometry and structure of normed linear spaces
46A55 Convex sets in topological linear spaces; Choquet theory
47L07 Convex sets and cones of operators
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