International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 19, Pages 1215-1231
Continuous homomorphisms of Arens-Michael algebras
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
Copyright © 2003 Alex Chigogidze. 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.
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.