Vol. 50, No. 1, 1974

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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