On extension of positive multilinear operators (Q6175233)

Let \(E_{1},\dots,E_{n}\) be separable Banach lattices with the subadditivity property. For every \(i=1,\dots,n\), consider \(G_{i}\) a majorizing subspace in \( E_{i}\). Let \(F\) be a topological vector lattice with the \(\sigma \)-interpolation property. The authors demonstrated that every positive multilinear operator \(T_{0}:G_{1}\times \dots \times G_{n}\longrightarrow F\) admits extension to a positive multilinear operator \(T:E_{1}\times \dots \times E_{n}\rightarrow F\). The proof was made using the linearization of positive multilinear operators by means of the Fremlin tensor product of vector lattices.