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.
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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.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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van Gaans, O., Kalauch, A. Tensor products of Archimedean partially ordered vector spaces. Positivity 14, 705–714 (2010). https://doi.org/10.1007/s11117-010-0085-5
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DOI: https://doi.org/10.1007/s11117-010-0085-5
Keywords
- Archimedean partially ordered vector space
- Fremlin tensor product
- Projective cone
- Riesz completion
- Tensor product