Topological algebras with orthogonal Schauder bases

Taqdir Husain and Saleem H. Watson

Vol. 91 (1980), No. 2, 339–347

DOI: 10.2140/pjm.1980.91.339

Abstract

Topological algebras with Schauder orthogonal bases are studied. Radicals, closed ideals and closed maximal ideals of such algebras are described. It turns out that a locally m-convex algebra with identity and having an orthogonal basis is metrizable. This implies that a complete locally m-convex algebra with an orthogonal basis and identity is algebraically and topologically isomorphic with the Fréchet algebra of all complex sequences.

Mathematical Subject Classification 2000

Primary: 46H05

Secondary: 46A35

Milestones

Received: 17 May 1979

Revised: 18 April 1980

Published: 1 December 1980