We show that the C∗ -dynamical system given by the so-called weakly monotone C∗ -algebra WM, 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 WM here exhibited.
Unique Ergodicity and Weakly Monotone Fock Space
Crismale V.
2022-01-01
Abstract
We show that the C∗ -dynamical system given by the so-called weakly monotone C∗ -algebra WM, 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 WM here exhibited.File in questo prodotto:
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