Multiplication operators on spaces of integrable functions with respect to a vector measure (Q2427289)

The authors study multiplication operators between \(L^p\)-spaces of vector measures, such as the spaces \(L_w^p(m)\) of weakly \(p\)-integrable functions and \(L_p(m)\) of \(p\)-integrable functions with \(1 \leq p \leq \infty\) and a countably additive measure \(m\) defined on a \(\sigma\)-algebra \(\Sigma\) of subsets of some set \(\Omega\) and taking values in a real Banach space \(X\). The majority of the results establish necessary and sufficient conditions on a function \(g \in L^p(m)\), so that the multiplication operator \(M_g f = g \cdot f\) is a bounded linear operator from one of the above spaces to another.