Tensor products of Archimedean partially ordered vector spaces
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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.
KeywordsArchimedean partially ordered vector space Fremlin tensor product Projective cone Riesz completion Tensor product
Mathematics Subject Classification (2000)06F20 46A40
O. van Gaans acknowledges the support by a ‘VIDI subsidie’ (639.032.510) in the ‘Vernieuwingsimpuls’ programme of the Netherlands Organisation for Scientific Research (NWO). The authors thank J.J. Grobler whose questions inspired this work.
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