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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/412751
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