Positivity

, Volume 14, Issue 4, pp 705–714 | Cite as

Tensor products of Archimedean partially ordered vector spaces

Open Access
Article

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 XY is contained in an Archimedean cone. The smallest Archimedean cone containing the projective cone satisfies an appropriate universal mapping property.

Keywords

Archimedean partially ordered vector space Fremlin tensor product Projective cone Riesz completion Tensor product 

Mathematics Subject Classification (2000)

06F20 46A40 

Notes

Acknowledgments

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.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Mathematical InstituteLeiden UniversityLeidenThe Netherlands
  2. 2.Institut für Analysis, Fachrichtung MathematikTU DresdenDresdenGermany

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