A corona theorem for countably many functions on a class of infinitely connected domains. (English) Zbl 0687.30025

Wang, Jian

Chin. Ann. Math., Ser. B 9, No. 4, 494-499 (1988).

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

Keywords:

corona theorem; countably many functions; infinitely connected domain