Holomorphic mappings associated to composition ideals of polynomials

Abstract

Many operator ideals $\mathcal{I}$ can be naturally associated to polynomial ideals $\mathcal{Q}$. In this paper we initiate a research program whose aim is to relate those holomorphic mappings $f$ that admit factorizations $f=u\circ g$, where $u\in \mathcal{I}$ and $g$ is holomorphic, with those $f$ whose derivative belongs to the associated composition polynomial ideal $\mathcal{Q}=\mathcal{I}\circ \mathcal{P}$.