International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 3, Pages 489-495
doi:10.1155/S0161171295000627

Fréchet algebras generated by certain of their elements

S. Ouzomgi,1 L. Redlin,1 and S. Watson2

1Department of Mathematics, The Pennsylvania State University, Abington 19001, PA, USA
2Departnent of Mathematics, California State University, Long Beach 90840, CA, USA

Received 26 April 1993; Revised 2 August 1993

Copyright © 1995 S. Ouzomgi et al. 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.

Abstract

We consider F-algebras A that are generated by elements of the form z, (z−λ1e)−1,…,(z−λNe)−1, where e is the identity. If A has no topclogical divisors of zero we show that A is isomorphic to H(Ω), where Ω is finitely connected region. We also study F-algebras in which {e,z,z−1,z2,z−2,…} is basis.