EXTENSION OF MULTILINEAR MAPPINGS ON BANACH-SPACES

By following an idea of Nicodemi we study certain sequences of extensi on operators for multilinear mappings on Banach spaces starting from a ny given extension operator for linear mappings. In this way we obtain several new properties of the extension operators previously studied by Aron, Berner, Cole, Davie and Gamelin. As an application of our met hods we show the existence of plenty of unbounded scalar-valued homomo rphisms on the locally convex algebra of all continuous polynomials on each infinite-dimensional Banach space. This improves a result of Dix on.