Orthogonal primitive idempotents and Banach algebras isomorphic with l₂

Taqdir Husain

Vol. 117 (1985), No. 2, 313–327

DOI: 10.2140/pjm.1985.117.313

Abstract

In this paper, a study of orthogonal primitive idempotents and minimal ideals in topological algebras with orthogonal bases has been made. Among other results, a structure theorem for Banach algebras with orthogonal bases has been proved, similar to Ambrose’s structure theorem for H^∗-algebras in the separable case. Furthermore, a necessary and sufficient condition is given for Banach algebras with orthogonal bases to be isomorphically homeomorphic with the Hilbert algebra l₂.

Mathematical Subject Classification 2000

Primary: 46H20

Secondary: 46J35

Milestones

Received: 4 August 1983

Revised: 29 September 1983

Published: 1 April 1985