Vol. 86, No. 2, 1980

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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