Vol. 31, No. 2, 1969

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Tensor products of compact convex sets

Isaac Namioka and Robert Ralph Phelps

Vol. 31 (1969), No. 2, 469–480

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.

Mathematical Subject Classification
Primary: 46.01
Received: 4 October 1968
Published: 1 November 1969
Isaac Namioka
Robert Ralph Phelps