Uniform Convergence of Cesaro Averages for Uniquely Ergodic C*-Dynamical Systems
Keyword(s):
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.
2018 ◽
Keyword(s):
2016 ◽
Vol 17
(01)
◽
pp. 1750007
◽
2019 ◽
Vol 41
(2)
◽
pp. 494-533
◽
2011 ◽
Vol 22
(01)
◽
pp. 1-23
◽
2010 ◽
Vol 47
(2)
◽
pp. 155-174
Keyword(s):
2020 ◽
pp. 96-182