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Trace states and KMS states for approximately inner dynamical one-parameter groups of *-automorphisms

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Abstract

The usual definition of approximately inner one-parameter groups of *-automorphisms ofC*-algebras (approximately inner dynamical one-parameter groups) contains a slight asymmetry. When this asymmetry is “corrected”, we show that if an approximately inner dynamical one-parameter group hasKMS states forone value of inverse temperature β=1/kT, then it hasKMS states for all values of β. By the Powers-Sakai Theorem it is enough to show that there is a trace state. We obtain a trace state as a limit of a sequence of “vector states” with respect to a givenKMS state and thus solve a problem raised in [6].

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Authors and Affiliations

  1. Department of Mathematics, University of Pennsylvania, 19174, Philadelphia, PA, USA

    Palle E. T. Jørgensen

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  1. Palle E. T. Jørgensen
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Communicated by H. Araki

Supported by Odense University, Denmark

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Jørgensen, P.E.T. Trace states and KMS states for approximately inner dynamical one-parameter groups of *-automorphisms. Commun.Math. Phys. 53, 135–142 (1977). https://doi.org/10.1007/BF01609127

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  • DOI: https://doi.org/10.1007/BF01609127

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