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. Ouzomgi1 , L. Redlin1 and S. Watson3

1Department of Mathematics, The Pennsylvania State University, Abington 19001, PA, USA
 3Departnent of Mathematics, California State University, Long Beach 90840, CA, USA

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.