Vol. 23, No. 3, 1967

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Automorphisms of postliminal Cāˆ—-algebras

E. Christopher Lance

Vol. 23 (1967), No. 3, 547ā€“555

Let α(A) denote the group of automorphisms of a C. algebra A. The object of this paper is to give an intrinsic algebraic characterization of those elements α of α(A) which are induced by a unitary operator in the weak closure of A in every faithful representation, and it is attained for the class of C-algebras known as GCR, or more recently postliminal. The relevant condition is that α should map closed two-sided ideals of A into themselves, and the main theorem (Theorem 2) may be thought of as an analogue for C-algebras of Kaplansky’s theorem for von Neumann algebras, namely that an automorphism of a Type I von Neumann algebra is inner if and only if it leaves the centre elementwise fixed. The proof of Theorem 2 requires the—probably unnecessary—assumption that A is separable.

Mathematical Subject Classification
Primary: 46.65
Received: 17 January 1967
Published: 1 December 1967
E. Christopher Lance