Absolute Schauder Decompositions and Linearization of Holomorphic Mappings of Bounded Type

Abstract

This paper has a twofold purpose: (i) to prove that the linearization of a holomorphic function of bounded type can be represented by means of the linearizations of its derivatives; (ii) to characterize when the identity operator on the predual $G_b(U)$ of the space of holomorphic functions of bounded type on a balanced open subset $U$ of a Banach space belongs to a given closed operator ideal. These two results rely on the existence of an $\mathcal{S}$-absolute Schauder decomposition for $G_b(U)$.