International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1989 / Article

Open Access

Volume 12 |Article ID 463292 | 4 pages |

A characterization of the algebra of holomorphic functions on a simply connected domain

Received03 Aug 1987


Let A be a singly-generated ℱ-algebra. It is shown that A isomorphic to H(Ω) where Ω is a simply connected domain in ℂ if and only if A has no topological divisors of zero. It follows from this that there are exactly three ℱ-algebras (up to isomorphism) which are singly generated and have no topological divisors of zero.

Copyright © 1989 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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