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Linearization of bounded holomorphic mappings on Banach spaces. (English) Zbl 0747.46038
The author shows that for every open subset U of a Banach space there exists a unique Banach space G (U) and a holomorphic mapping g u :UG (U) such that every Banach valued bounded holomorphic function on U can be written as a composition of g u and a Banach valued continuous linear mapping on G (U). This gives a linearization of bounded holomorphic mappings and shows that H (U) has the structure of a dual Banach space. Applications to the study of holomorphic mappings of compact type, the approximation property and polynomials are given using this linearization result.
Reviewer: S.Dineen

MSC:
46G20Infinite dimensional holomorphy
46E50Spaces of differentiable or holomorphic functions on infinite-dimensional spaces
46B28Spaces of operators; tensor products; approximation properties