Article

Positivity

, Volume 14, Issue 4, pp 705-714

Open Access This content is freely available online to anyone, anywhere at any time.

Tensor products of Archimedean partially ordered vector spaces

  • Onno van GaansAffiliated withMathematical Institute, Leiden University Email author 
  • , Anke KalauchAffiliated withInstitut für Analysis, Fachrichtung Mathematik, TU Dresden

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