Vol. 86, No. 2, 1980

Recent Issues
Vol. 325: 1
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Vol. 319: 1  2
Vol. 318: 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 Naimark-related to -representations; a correction: “When is a representation of a Banach -algebra Naimark-related to a -representation?”

Bruce Alan Barnes

Vol. 86 (1980), No. 2, 397–402

Let A be a Banach -algebra. A theorem is proved concerning a sufficient condition for a continuous representation of A on a Hilbert space H to be Naimark-related to a -representation of A on H. One corollary of this result is that a continuous (topologically) irreducible representation of A on H is Naimark-related to a -representation of A on H if and only if some coefficient of the representation is a nonzero positive functional of A.

One purpose of the paper is to correct in part a previously published result the proof of which contains a serious gap.

Mathematical Subject Classification 2000
Primary: 46K10
Secondary: 46L05
Received: 27 February 1979
Revised: 17 July 1979
Published: 1 February 1980
Bruce Alan Barnes