On ideals of polynomials and multilinear mappings between Banach spaces (Q1423791)

It is shown that for every quasi-normed ideal \({\mathcal Q}\) of \(n\)-homogeneous continuous polynomials between Banach spaces, there is a quasi-normed ideal \({\mathcal A}\) of \(n\)-linear continuous mappings such that \(q \in {\mathcal Q}\) if and only if the associated \(n\)-linear mapping \(\check{q}\) of \(q\) is in \({\mathcal A}\). Completeness, maximality, and minimality of the ideals are preserved under the given construction.