Extension of multilinear mappings on Banach spaces

By following an idea of Nicodemi we study certain sequences of extension operators for multilinear mappings on Banach spaces starting from any given extension operators previously studied by Aron, Berner, Cole, Davie and Gamelin. As an application of our methods we show the existence of plenty of unbounded scalar-valued homomorphisms on the locally convex algebra of all continuous polynomials on each infinite-dimensional Banach space. This improves a result of Dixon.