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Uniform Convergence of Cesaro Averages for Uniquely Ergodic $C^*$-Dynamical Systems
Version 1
: Received: 20 November 2018 / Approved: 22 November 2018 / Online: 22 November 2018 (04:17:04 CET)
A peer-reviewed article of this Preprint also exists.
Fidaleo, F. Uniform Convergence of Cesaro Averages for Uniquely Ergodic C*-Dynamical Systems. Entropy 2018, 20, 987. Fidaleo, F. Uniform Convergence of Cesaro Averages for Uniquely Ergodic C*-Dynamical Systems. Entropy 2018, 20, 987.
Abstract
Consider a uniquely ergodic $C^*$-dynamical system ba\-sed on a unital $*$-endomorphism $\Phi$ of a $C^*$-algebra. We prove the uniform convergence of Cesaro averages $\frac1{n}\sum_{k=0}^{n-1}\lambda^{-n}\Phi(a)$ for all values $\lambda$ in the unit circle which are not eigenvalues corresponding to "measurable non continuous" eigenfunctions. This result generalises the analogous one in commutative ergodic theory presented in [19], which turns out to be a combination of the Wiener-Wintner Theorem (cf. [22]) and the uniformly convergent ergodic theorem of Krylov and Bogolioubov (cf. [15]).
Keywords
ergodic theorems; C*-dynamical systems
Subject
Computer Science and Mathematics, Analysis
Copyright: 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.
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