Analytic representations of dominated bilinear operators (Q1921837)

A linear isometry is established between a space of dominated operators on a product space and an appropriate space of linear operators. Specifically, for Banach spaces \(X\) and \(Y\), let \(Z\) denote the projective tensor product of \(X\) and \(Y\). Given an arbitrary \(K\)-space \(E\), \({\mathcal L}_A(Z,E)\) denotes the space of linear operators with the corresponding norm and \({\mathcal B}_A(X,Y;E)\) denotes the dominated operators acting on the product of \(X\) and \(Y\). An isometry is established between \({\mathcal L}_A(Z,E)\) and \({\mathcal B}_A(X,Y;E)\).