Fr�chet algebras of finite type

Abstract

The main objects of study in this paper are Frechet algebras having an Arens Michael representation in which every Banach algebra is finite dimensional. We shall classify these algebras using a theorem which ensures that the image of any continuous linear map of a Frechet space of finite type (i.e., for which the defining seminorms have a finite dimensional cokernel) into any Frechet space is in fact closed.