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Theorems of Krein Milman type for certain convex sets of functions operators

Robert R. Phelps — 1970

Annales de l'institut Fourier

Sufficient conditions are given in order that, for a bounded closed convex subset B of a locally convex space E , the set C ( X , B ) of continuous functions from the compact space X into B , is the uniformly closed convex hull in C ( X , E ) of its extreme points. Applications are made to the unit ball of bounded (or compact, or weakly compact) operators from certain Banach spaces into C ( X ) .

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