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Entropy 2018, 20(12), 987; https://doi.org/10.3390/e20120987

Uniform Convergence of Cesaro Averages for Uniquely Ergodic C*-Dynamical Systems

Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Roma, Italy
Received: 20 November 2018 / Revised: 9 December 2018 / Accepted: 11 December 2018 / Published: 19 December 2018
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Abstract

Consider a uniquely ergodic C * -dynamical system based on a unital *-endomorphism Φ of a C * -algebra. We prove the uniform convergence of Cesaro averages 1 n k = 0 n 1 λ n Φ ( a ) for all values λ in the unit circle, which are not eigenvalues corresponding to “measurable non-continuous” eigenfunctions. This result generalizes an analogous one, known in commutative ergodic theory, which turns out to be a combination of the Wiener–Wintner theorem and the uniformly convergent ergodic theorem of Krylov and Bogolioubov. View Full-Text
Keywords: ergodic theorems; C*-dynamical systems ergodic theorems; C*-dynamical systems
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Fidaleo, F. Uniform Convergence of Cesaro Averages for Uniquely Ergodic C*-Dynamical Systems. Entropy 2018, 20, 987.

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