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.
