On functional representation of locally m ‐pseudoconvex algebras

Source abstract

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 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 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.