A spectral characterization of universally weakly inner automorphisms of separable 𝐶*-algebras

Wright, Steve

doi:10.1090/S0002-9939-1983-0706517-4

A spectral characterization of universally weakly inner automorphisms of separable $C^{\ast }$-algebras
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Proc. Amer. Math. Soc. 89 (1983), 91-94 Request permission

Abstract:

Let $A$ be a separable ${C^ * }$-algebra, $\alpha$ a $*$-automorphism of $A$. The following theorem is proven: $\alpha$ is weakly inner in every faithful, nondegenerate representation of $A$ if and only if $\alpha$ fixes each closed, two-sided ideal of $A$ and the Borchers spectrum of each quotient automorphism vanishes.

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