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The approximation property for spaces of holomorphic functions on infinite-dimensional spaces. I. (English) Zbl 1060.41031

Let \(U\) be an open set of a separable Fréchet space with the bounded approximation property. Then the space of holomorphic functions on \(U\) endowed with compact-open topology has the approximation property. The result is also applied to characterize the spectra of some algebras of holomorphic mappings with values in a Banach algebra.

MSC:

41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
46A04 Locally convex Fréchet spaces and (DF)-spaces
46J40 Structure and classification of commutative topological algebras
46E10 Topological linear spaces of continuous, differentiable or analytic functions

Keywords:

Fréchet space
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References:

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