Analytic generators and the KMS condition

De Cannière, Jean

doi:10.1090/S0002-9939-1983-0695260-6

Analytic generators and the KMS condition
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by Jean De Cannière PDF

Proc. Amer. Math. Soc. 88 (1983), 287-292 Request permission

Abstract:

The KMS condition at arbitrary $\beta$ for a state $\omega$ of a ${C^ * }$-dynamical system $(A,{\mathbf {R}},\alpha )$ is stated in terms of the analytic continuation of the correlation functions $t \mapsto \omega ({x^ * }{\alpha _t}(x))(x \in A){\text {in}} - i({\text {or}} + i)$. The precise formulation involves the analytic generator of $\alpha$ (or its inverse).

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