01-251 Vojkan Jaksic, Claude-Alain Pillet
A Note on Eigenvalues of Liouvilleans (58K, postscript) 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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