Orthogonal bases are Schauder bases and a characterization of Φ-algebras

Sherif El-Helaly and Taqdir Husain

Vol. 132 (1988), No. 2, 265–275

DOI: 10.2140/pjm.1988.132.265

Abstract

It is shown that every orthogonal basis in a topological algebra is a Schauder basis. A new class of topological algebras called Φ-algebras is introduced. They are characterized in terms of seminorms. Among other results, a necessary and sufficient condition for a locally convex s-algebra with an unconditional orthogonal basis to be an A-convex algebra is given.

Mathematical Subject Classification 2000

Primary: 46J05

Secondary: 46A35, 46A45, 46H05

Milestones

Received: 29 November 1986

Revised: 20 July 1987

Published: 1 April 1988