Holomorphic mappings associated to composition ideals of polynomials

Abstract

Many operator ideals ℐ can be naturally associated to polynomial ideals Q. In this paper we initiate a research program whose aim is to relate those holomorphic mappings f that admit factorizations f = u_∘_g, where u ∈ ℐ and g is holomorphic, with those f whose derivative belongs to the associated composition polynomial ideal Q = ℐ ∘ ℘.