Aqzzouz, Belmesnaoui Spaces of continuous functions taking their values in the \(\varepsilon\)-product. (English) Zbl 1116.46002 RACSAM, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 99, No. 2, 143-148 (2005). The author deals with linear spaces endowed with a bornology consisting of Banach disks in the sense of H.Hogbe–Nlend and L.Waelbroeck, and calls them \(b\)-spaces. He defines nuclearity as well as the \(\varepsilon\)-product in the class of \(b\)-spaces. Then he proves his main result: Theorem. Let \(X\) be a compact or locally compact \(\sigma\)-compact topological space, let \(N\) be a nuclear \(b\)-space, and let \(E\) be a \(b\)-space. Then the spaces of continuous vector-valued functions \(C(X,N\varepsilon E)\) and \(N\varepsilon C(X,E)\) are naturally isomorphic as \(b\)-spaces. Reviewer: Susanne Dierolf (Trier) Cited in 1 Document MSC: 46A32 Spaces of linear operators; topological tensor products; approximation properties 46M05 Tensor products in functional analysis 46A17 Bornologies and related structures; Mackey convergence, etc. Keywords:tensor products; spaces with a bornology; nuclearity Citations:Zbl 0139.06902 PDFBibTeX XMLCite \textit{B. Aqzzouz}, RACSAM, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 99, No. 2, 143--148 (2005; Zbl 1116.46002) Full Text: EuDML