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Characterization of approximately inner automorphisms


Author: Marie Choda
Journal: Proc. Amer. Math. Soc. 84 (1982), 231-234
MSC: Primary 46L40
DOI: https://doi.org/10.1090/S0002-9939-1982-0637174-2
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.


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

  • [1] M. Choda, The states associated with approximately inner automorphisms, Proc. Amer. Math. Soc. 81 (1981), 343-344. MR 593488 (81m:46088)
  • [2] A. Connes, Classification of injective factors, Ann. of Math. (2) 104 (1976), 73-115. MR 0454659 (56:12908)
  • [3] -, A factor of type $ {\text{I}}{{\text{I}}_1}$ with countable fundamental group, J. Operator Theory 4 (1980), 151-153. MR 587372 (81j:46099)
  • [4] J. Dixmier, Formes linéaires sur un anneau d'opérateurs, Bull. Soc. Math. France 81 (1953), 9-39. MR 0059485 (15:539a)
  • [5] S. Sakai, Automorphisms and tensor products of operator algebras, Amer. J. Math. 97 (1975), 889-896. MR 0390787 (52:11610)
  • [6] R. Schatten, Norm ideals of completely continuous operators, Springer-Verlag, Berlin and New York, 1970. MR 0257800 (41:2449)
  • [7] I. Segal, A non-commutative extension of abstract integration, Ann. of Math. 57 (1953), 401-457. MR 0054864 (14:991f)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0637174-2
Keywords: Factor, automorphism, state
Article copyright: © Copyright 1982 American Mathematical Society

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