Representation of Topological Algebras by Projective Limit of Fréchet Algebras

Abstract

It is shown that every topological Hausdorff algebra (in particular, locally pseudoconvex Hausdorff algebra) $A$ with jointly continuous multiplication is topologically isomorphic to a dense subalgebra of the projective limit of Fréchet (respectively, locally pseudoconvex Fréchet) algebras. In case, when $A$ is complete, $A$ and this projective limit of Fréchet (respectively, locally pseudoconvex Fréchet) algebras are topologically isomorphic. A partly new proof for these results from [11] are given.