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arXiv · 2108.11938

Invariant Conditional Expectations and Unique Ergodicity for Anzai Skew-Products

Simone Del Vecchio·Francesco Fidaleo·Stefano Rossi
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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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Simone Del Vecchio, Francesco Fidaleo, Stefano Rossi. 2021-08-26. Invariant Conditional Expectations and Unique Ergodicity for Anzai Skew-Products. https://arxiv.org/abs/2108.11938

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