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Proceedings of the American Mathematical Society

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

 
 

 

The states associated with approximately inner automorphisms


Author: Marie Choda
Journal: Proc. Amer. Math. Soc. 81 (1981), 343-344
MSC: Primary 46L40
DOI: https://doi.org/10.1090/S0002-9939-1981-0593488-5
MathSciNet review: 593488
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Abstract: Let $ M$ be a $ {\text{I}}{{\text{I}}_1}$-factor acting standardly on a Hilbert space $ H$. For an approximately inner automorphism $ \theta $ of $ M$, there exists a state $ \varphi $ on $ B(H)$ associated with $ \theta $. If the symmetry $ \sigma $ of $ M \otimes M$ is approximately inner on $ M \otimes M$, then, by restricting the state associated with $ \sigma $ to $ B(H) \otimes I$, we have a hypertrace of $ M$.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0593488-5
Keywords: $ {\text{I}}{{\text{I}}_1}$-factor, trace, state, involution
Article copyright: © Copyright 1981 American Mathematical Society

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