Vol. 50, No. 1, 1974

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
Representations of B∗-algebras on Banach spaces

Bruce Alan Barnes

Vol. 50 (1974), No. 1, 7–18

This paper deals with continuous irreducible representations of a B-algebra on a Banach space. The main result is that if π is a continuous irreducible representation of a B-algebra A on a reflexive Banach space X, and if there is a subset S of A such that the intersection of the mull spaces of the operators π(a) for all a S is a nonzero, finite dimensional subspace of X, then X is a Hilbert space in am equivalent norm and π is similar to a -representativn of A on this Hilbert space.

Mathematical Subject Classification 2000
Primary: 46K10
Received: 13 September 1972
Revised: 27 December 1972
Published: 1 January 1974
Bruce Alan Barnes