 01251 Vojkan Jaksic, ClaudeAlain Pillet
 A Note on Eigenvalues of Liouvilleans
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Jul 9, 01

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Abstract. Let $L$ be the Liouvillean of an ergodic quantum dynamical system
$({\mathfrak M}, \tau, \omega)$. We give a new proof of the theorem
of Jadczyk that eigenvalues of $L$ are simple and form a subgroup of
R. If $\omega$ is a $(\tau, \beta)$KMS state for some $\beta \not=0$
we show that this subgroup is trivial, namely that zero is the only
eigenvalue of $L$. Hence, for KMS states ergodicity is equivalent to
weak mixing.
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