Anzai skew-products are shown to be uniquely ergodic with respect to the fixed-point subalgebra if and only if there is a unique conditional expectation onto such a subalgebra which is invariant under the dynamics. For the particular case of skew-products, this solves a question raised by B. Abadie and K. Dykema in the wider context of C*-dynamical systems.
Invariant Conditional Expectations and Unique Ergodicity for Anzai Skew-Products
Del Vecchio Simone
;Rossi Stefano
2023-01-01
Abstract
Anzai skew-products are shown to be uniquely ergodic with respect to the fixed-point subalgebra if and only if there is a unique conditional expectation onto such a subalgebra which is invariant under the dynamics. For the particular case of skew-products, this solves a question raised by B. Abadie and K. Dykema in the wider context of C*-dynamical systems.File in questo prodotto:
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