Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
MathSciNet review: 706517
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46L40, 46L05

Retrieve articles in all journals with MSC: 46L40, 46L05

Additional Information

Keywords: Universally weakly inner automorphism, separable $ {C^ * }$-algebra, Connes spectrum, Borchers spectrum, ideal, hereditary $ {C^ * }$-subalgebra
Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society