Abstract
AbstractWe show that the \(C^*\)-dynamical system given by the so-called weakly monotone \(C^*\)-algebra \({\mathcal {W}\mathcal {M}}\), and the shift automorphism on it, is not uniquely ergodic. In fact, the fixed-point subalgebra with respect to such an action is trivial, whereas there are plenty of shift-invariant states. The last assertion is proved using a Hamel basis for the linear structure of a dense \(*\)-algebra of \({\mathcal {W}\mathcal {M}}\) here exhibited.KeywordsNon-commutative dynamical systemsUnique ergodicityWeakly monotone Fock spaces
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