Journal of Operator Theory

Volume 95, Issue 1, Winter 2026 pp. 77-102.

On the KMS states for the Bernoulli shift

Authors: Sundar Shanmugasundaram
Author institution: Institute of Mathematical Sciences (HBNI), CIT Campus, Taramani, Chennai-600113, India

Summary: Let $\Omega:=\{0,1\}^{\mathbb{Z}}$, and let $\tau:\Omega \to \Omega$ be the Bernoulli shift. For the flow on the crossed product $C(\Omega)\rtimes_\tau \mathbb{Z}$ determined by a potential that depends on only one coordinate, we show that for every $\beta \neq 0$, there is an extremal $\beta$-KMS state on $C(\Omega)\rtimes_\tau \mathbb{Z}$ of type II$_\infty$.

DOI: http://dx.doi.org/10.7900/jot.2024mar07.2468
Keywords: Bernoulli shift, KMS states, isometric representation

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