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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Characterization of approximately inner automorphisms


Author: Marie Choda
Journal: Proc. Amer. Math. Soc. 84 (1982), 231-234
MSC: Primary 46L40
MathSciNet review: 637174
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Abstract: Let $ M$ be a finite factor acting standardly on a Hilbert space $ H$. An automorphism $ \theta $ of $ M$ is approximately inner on $ M$ if and only if there exists a state $ \phi $ on $ B(H)$ such that $ \phi (JuJ\theta (u)) = 1 $ for every unitary $ u$ in $ M$, where $ J$ is the canonical involution. Specially, $ \theta $ is inner on $ M$ if and only if such a state is a vector state.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0637174-2
PII: S 0002-9939(1982)0637174-2
Keywords: Factor, automorphism, state
Article copyright: © Copyright 1982 American Mathematical Society