The states associated with approximately inner automorphisms
HTML articles powered by AMS MathViewer
- by Marie Choda PDF
- Proc. Amer. Math. Soc. 81 (1981), 343-344 Request permission
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
- A. Connes, Classification of injective factors. Cases $II_{1},$ $II_{\infty },$ $III_{\lambda },$ $\lambda \not =1$, Ann. of Math. (2) 104 (1976), no. 1, 73–115. MR 454659, DOI 10.2307/1971057
- Shôichirô Sakai, Automorphisms and tensor products of operator algebras, Amer. J. Math. 97 (1975), no. 4, 889–896. MR 390787, DOI 10.2307/2373678
Additional Information
- © Copyright 1981 American Mathematical Society
- 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