Affine functions on simplexes and extreme operators

IfK a simplex andX a Banach space thenA(K, X) denotes the space of affine continuous functions fromK toX with the supremum norm. The extreme points of the closed unit ball ofA(K, X) are characterized,X being supposed to satisfy certain conditions. This characterization is used to investigate the extreme compact operators from a Banach spaceX to the spaceA(K)=A(K, (− ∞, ∞)). This note is part of the author’s Ph.D. thesis prepared at the Hebrew University of Jerusalem under the supervision of Prof. A. Dvoretzky and Dr. J. Lindenstrauss. The author wishes to thank them for their helpful advice and kind encouragement.