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

DOI: 10.2140/pjm.1980.86.397

Abstract

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

Milestones

Received: 27 February 1979

Revised: 17 July 1979

Published: 1 February 1980