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Proceedings of the American Mathematical Society

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The states associated with approximately inner automorphisms

Author: Marie Choda
Journal: Proc. Amer. Math. Soc. 81 (1981), 343-344
MSC: Primary 46L40
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$.

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

  • [1] A. Connes, Classification of injective factors. Cases 𝐼𝐼₁, 𝐼𝐼_{∞}, 𝐼𝐼𝐼_{𝜆}, 𝜆̸=1, Ann. of Math. (2) 104 (1976), no. 1, 73–115. MR 0454659
  • [2] Shôichirô Sakai, Automorphisms and tensor products of operator algebras, Amer. J. Math. 97 (1975), no. 4, 889–896. MR 0390787

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Keywords: $ {\text{I}}{{\text{I}}_1}$-factor, trace, state, involution
Article copyright: © Copyright 1981 American Mathematical Society