On ideals of polynomials and multilinear mappings between Banach spaces

摘要

It is shown that for every quasi-normed ideal ${cal Q}$ of n-homogeneous continuous polynomials between Banach spaces there is a quasi-normed ideal ${cal A}$ of n-linear continuous mappings ${cal A}$ such that $q in {cal Q}$ if and only if the associated n-linear mapping $check{q}$ of q is in ${cal A}$.