International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 1, Pages 65-68
A characterization of the algebra of holomorphic functions on a simply connected domain
Department of Mathematics and Computer Science, California State University, Long Beach 90840, California, USA
Received 3 August 1987
Copyright © 1989 Derming Wang and Saleem Watson. 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.
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.