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.
Tensor Product Bounded Variation Banach Lattice Riesz Space Norm Completeness
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