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 ∘ ℘.
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Richard M. Aron, Geraldo Botelho, Daniel Pellegrino, Pilar Rueda, Holomorphic mappings associated to composition ideals of polynomials. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 21 (2010), no. 3, pp. 261–274DOI 10.4171/RLM/571