Abstract
Let K be a compact Choquet simplex and A (K) the space of all continuous real-valued affine functions on K. Then A (K) is a partially ordered Banach space with the Riesz Decomposition Property and the dual A (K)* of A (K) is an L-space [I5 ]. In particular, if X is a compact Hausdorff space, then C(X) =A (K) where K is the compact convex set of probability measures on X in the weak*-topology [2 . In this paper certain relations between K, A (K) and A (K)* are studied. For example under certain conditions on K, A(K)* is a space of the type l1(D) if and only if the set Ke of extreme points of K contains no nonempty compact perfect subsets. The results presented here generalize some of the results in [6] and [13 ]. A sufficient condition for A (K) to have the Dieudonne property is also presented.
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