Some properties of the \(\varepsilon_{\infty }\)-product of quotient bornological spaces (Q946076)

The main result of this paper is the following theorem on the \(\varepsilon\)-product of Schwartz in the category of quotient bornological spaces. Let \(N\) be an \(\mathcal{L}_{\infty}\)-space, let \(G\) be a Banach space and let \(E| F\) be a quotient bornological space, then \(G \varepsilon_{\infty} (N \varepsilon (E| F))\) and \(N \varepsilon (G \varepsilon_{\infty} (E| F))\) are isomorphic. Here \(\varepsilon_{\infty}\) denotes a tensor product defined by the first author. Some consequences are mentioned.