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On the isomorphic classification of weighted spaces of holomorphic functions. (English) Zbl 0965.46012

Summary: We show that there are only two isomorphism classes for weighted spaces of holomorphic functions on the unit disk with moderately decreasing weights. In particular, a space of holomorphic functions with a weighted sup-norm here is either isomorphic to \(\ell_\infty\) or to \(H_\infty\) depending on special properties of the weight which can be easily checked.

MSC:

46E10 Topological linear spaces of continuous, differentiable or analytic functions
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