Isomorphisms of spaces of continuous affine functions on compact convex sets with Lindelöf boundaries

Abstract

Let X, Y be compact convex sets such that every extreme point of X and Y is a weak peak point and both ext X and ext Y are Lindelof spaces. We prove that if there exists an isomorphism T: U c (X) → U c (Y) with ∥T∥·∥T -1 ∥ < 2, then ext X is homeomorphic to ext Y. This generalizes results of C. H. Chu and H. B. Cohen.