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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