International Journal of Mathematics and Mathematical Sciences 
Volume 2003 (2003), Issue 19, Pages 1215-1231
doi:10.1155/S0161171203012237

Continuous homomorphisms of Arens-Michael algebras

Alex Chigogidze

 Department of Mathematics and Statistics, University of Saskatchewan, McLean Hall, 106 Wiggins Road, Saskatchewan, Saskatoon S7N 5E6, Canada
Received 3 March 2001; Revised 3 July 2001

Abstract

It is shown that every continuous homomorphism of Arens-Michael algebras can be obtained as the limit of a morphism of certain projective systems consisting of Fréchet algebras. Based on this, we prove that a complemented subalgebra of an uncountable product of Fréchet algebras is topologically isomorphic to the product of Fréchet algebras.