Consider a uniquely ergodic C∗-dynamical system ba-sed on a unital ∗-endomorphism Φ of a C∗-algebra. We prove the uniform convergence of Cesaro averages 1n∑n−1k=0λ−nΦ(a) for all values λ 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]).
Fidaleo, F. (2018). Uniform convergence of Cesaro averages for uniquely ergodic C∗-dynamical systems. ENTROPY, 20, 987 [10.3390/e20120987].
Uniform convergence of Cesaro averages for uniquely ergodic C∗-dynamical systems
Francesco Fidaleo
2018-12-01
Abstract
Consider a uniquely ergodic C∗-dynamical system ba-sed on a unital ∗-endomorphism Φ of a C∗-algebra. We prove the uniform convergence of Cesaro averages 1n∑n−1k=0λ−nΦ(a) for all values λ 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]).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
