Suppose that 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 K2. We compare these
different tensor products and their extreme points; in doing so, we obtain some new
characterizations of Choquet simplexes, another formulation of Grothendieck’s
approximation problem and much simpler proofs of known characterizat-ions of the
extreme points of these tensor products. Mosi 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.
