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

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.