International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 2, Pages 223-237

On functional representation of locally m-pseudoconvex algebras

Jorma Arhippainen

Department of Mathematical Sciences, University of Oulu, P.O. Box 400, Oulu SF-90570, Finland

Received 4 February 1997; Revised 26 December 1997

Copyright © 1999 Jorma Arhippainen. 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.


Functional representation of a topological algebra (A,T) has been studied in many papers under various assumptions for the topology T on A. Usually the image Aˆ of the Gelfand map has been equipped with the compact-open topology. This leads, in several cases, to such kind of difficulties as, for instance, that the Gelfand map is not necessarily continuous or that the compact-open topology is not of the same type as the topology T. In this paper, we study locally m-pseudoconvex algebras and provide Aˆ with such kind of topology that the above two claims are fulfilled. By using this representation the description of the closed ideals of (A,T) is studied.