Representations of Topological Algebras by Projective Limits

It is shown that a) it is possible to define the topology of any topological algebra by a collection of F -seminorms, b) every complete locally uniformly absorbent (complete locally A-pseudoconvex) Hausdorff algebra is topologically isomorphic to a projective limit of metrizable locally uniformly absorbent algebras (respectively, A-(k-normed) algebras, where k ∈ (0, 1] varies, c) every complete locally idempotent (complete locally m-pseudoconvex) Hausdorff algebra is topologically isomorphic to a projective limit of locally idempotent Fréchet algebras (respectively, k-Banach algebras, where k ∈ (0, 1] varies) and every m-algebra is locally m-pseudoconvex. Condition for submultiplicativity of F -seminorm is given. 1 Institute of Mathematics, University of Tartu, 2 J. Liivi Str., room 614, 50409 Tartu, Estonia. E-mail address: [email protected] Date: Received: 29 August 2010; Accepted: 12 November 2010. 2010 Mathematics Subject Classification. Primary 46H05; Secondary 46H20.