Tensor products of compact convex sets

Abstract

Suppose thai K1 and K2 are compact convex subsets of locally convex spaces E1 and E2 respectively. There are several definitions of new compact convex sets associated with K1 and K2, each of which may reasonably be called a “ tensor product ” of K1 and K2a We compare these different tensor products and their extreme points in doing so, we obtain some new characterizations of Choquefc simpiexes, another formulation of Grothendieck’s approximation problem and much simpler proofs of known characterizations of the extreme points of these tensor products. Most of these results are obtained as special cases of theorems in the first half of the paper which deal with the state spaces of tensor products of partially ordered linear spaces with order unit. © 1969 by Pacific Journal of Mathematics.