Tensor products of Archimedean partially ordered vector spaces

Abstract

We study the tensor product of two directed Archimedean partially ordered vector spaces X and Y by means of Riesz completions. With the aid of the Fremlin tensor product of the Riesz completions of X and Y we show that the projective cone in X ⊗ Y is contained in an Archimedean cone. The smallest Archimedean cone containing the projective cone satisfies an appropriate universal mapping property. © 2010 The Author(s).