Positivity

, Volume 14, Issue 4, pp 705–714

Tensor products of Archimedean partially ordered vector spaces

Open AccessArticle

DOI: 10.1007/s11117-010-0085-5

Cite this article as:
van Gaans, O. & Kalauch, A. Positivity (2010) 14: 705. doi:10.1007/s11117-010-0085-5

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 spaceFremlin tensor productProjective coneRiesz completionTensor product

Mathematics Subject Classification (2000)

06F2046A40
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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