Multilinear mappings versus homogeneous polynomials and a multipolynomial polarization formula

Abstract

We show that (k, m)-linear mappings, introduced by I. Chernega and A. Zagorodnyuk in [3], are particular cases of polynomials. As corollaries, we expose some apparently overlooked properties in the literature. For instance, every multilinear mapping is a homogeneous polynomial. Contributions to the polarization formula are also provided.2010 Mathematics Subject Classification. Primary 46G20, 46G25, 47H60; Secondary 15A99 .