Tensor products of Archimedean Riesz spaces: A representational approach
Year: 2025
Type: article
Abstract: In an earlier paper, Buskes and the author pointed out that, given two Archimedean Riesz spaces E E and F F , it is relatively simple to construct, from their Ogasawara-Maeda representations, a third Archimedean Riesz space G G and a bi-injective Riesz bimorphism ϕ : E × F → G \phi :E\times F\to G . They further pointed out that the Riesz subspace of G G generated by ϕ ( E × F ) \phi (E\times F) is isomorphic to the Archimedean Riesz space tensor product E ⊗ ¯ F E\overline {\otimes }F constructed by Fremlin. The proof there relies on the properties of E ⊗ ¯ F E\overline {\otimes }F proved by Fremlin. In this paper we show that this approach actually gives a simple way to construct and establish the properties of E ⊗ ¯ F E\overline {\otimes }F and that any choice of G G and ϕ \phi yield isomorphic objects.
DOI: 10.1090/bproc/251
Author: A. Wickstead
Institution: Queen's University Belfast
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $750
OpenAlex ID: W4408508754