Factorization of holomorphic mappings on 𝐶(𝐾)-spaces

Taskinen, Jari

doi:10.1090/S0002-9939-97-03824-0

Factorization of holomorphic mappings on $C(K)$-spaces
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Proc. Amer. Math. Soc. 125 (1997), 2337-2346 Request permission

Abstract:

We prove a universal mapping theorem for a large class of holomorphic mappings $F$ on a $C(K)$–space, stating that $F$ can be locally written in the form $F(f) = B \bigl ( 1 /( 1 - Af) \bigr ),$ where $A$ and $B$ are bounded linear operators on certain Banach spaces consisting of functions on $K$, and the division is taken pointwise.

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