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

1432-0916

Springer Online Journal Archives 1860-2000

Mathematics

Physics

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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