Based on the Archimedeanization developed by Paulsen and Tomforde, we give an explicit description for the positive cones of maximal tensor products of function systems. From this description, we obtain an approximation theorem for nuclear maps between function systems. As an application, we give elementary proofs on several characterizations of nuclear function systems that are already known.
KeywordsFunction system Archimedean ordered space Archimedean ordered \(*\)-vector space Tensor product Nuclear
Mathematics Subject Classification46B40 46B28
- 3.Effros, E.G.: Injectives and Tensor Products for Convex Sets and \(C^*\)-Algebras. University College of Swansea, NATO Advanced Study Institute, Swansea (1972)Google Scholar
- 9.Kadison, R.V.: A representation theory for commutative topological algebra. Mem. Am. Math. Soc. 1951(7) (1951)Google Scholar
- 15.Paulsen, V.I., Todorov, I.G., Tomforde, M.: Operator system structures on ordered spaces. Proc. London Math. Soc. 102(3), 25–49 (2011)Google Scholar