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A spectral characterization of universally weakly inner automorphisms of separable $ C\sp{\ast} $-algebras


Author: Steve Wright
Journal: Proc. Amer. Math. Soc. 89 (1983), 91-94
MSC: Primary 46L40; Secondary 46L05
DOI: https://doi.org/10.1090/S0002-9939-1983-0706517-4
MathSciNet review: 706517
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0706517-4
Keywords: Universally weakly inner automorphism, separable $ {C^ * }$-algebra, Connes spectrum, Borchers spectrum, ideal, hereditary $ {C^ * }$-subalgebra
Article copyright: © Copyright 1983 American Mathematical Society