Abstract
We construct the bornological Riesz space tensor product of two bornological Riesz spaces. This unifies the Archimedean Riesz space tensor product and the projective tensor product, both introduced by Fremlin. We extend the results, even in these special cases, by considering maps of bounded variation rather than positive maps. This note is without proofs, but the proof and complete bornology background of a similar result are discussed elsewhere in this volume.
The first author acknowledges support from Office of Naval Research grant ONR N00014–01–10322, in the Summer of 2001. Both authors acknowledge support from NATO CRG grant 940605.
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Buskes, G., van Rooij, A. (2002). The Bornological Tensor Product of two Riesz Spaces. In: Martínez, J. (eds) Ordered Algebraic Structures. Developments in Mathematics, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3627-4_1
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DOI: https://doi.org/10.1007/978-1-4757-3627-4_1
Publisher Name: Springer, Boston, MA
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