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A corona theorem for countably many functions on a class of infinitely connected domains. (English) Zbl 0687.30025
Let D be a domain in the complex plane, and let \(H^{\infty}(D)\) be the algebra of bounded analytic functions on D. Let \({\mathcal M}(D)\) be the maximal ideal space of \(H^{\infty}(D)\), the domain can be identified with an open subset of \({\mathcal M}(D)\). The author shows that D is uniformly dense in \({\mathcal M}(D)\), that is, a corona theorem for countably many functions on some infinitely connected domain.
Reviewer: T.Nakazi
MSC:
30D55 \(H^p\)-classes (MSC2000)
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
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