Characterization of approximately inner automorphisms

Choda, Marie

doi:10.1090/S0002-9939-1982-0637174-2

Characterization of approximately inner automorphisms
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by Marie Choda

Proc. Amer. Math. Soc. 84 (1982), 231-234

DOI: https://doi.org/10.1090/S0002-9939-1982-0637174-2

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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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