Power bounded operators and the mean ergodic theorem for subsequences

0532219 - MÚ 2022 RIV US eng J - Článek v odborném periodiku
Eisner, T. - Müller, Vladimír
Power bounded operators and the mean ergodic theorem for subsequences.
Journal of Mathematical Analysis and Applications. Roč. 493, č. 1 (2021), č. článku 124523. ISSN 0022-247X. E-ISSN 1096-0813
Grant CEP: GA ČR(CZ) GX20-31529X
Institucionální podpora: RVO:67985840
Klíčová slova: Hardy functions * mean ergodic theorem for subsequences * power bounded operators * weighted ergodic theorem
Obor OECD: Pure mathematics
Impakt faktor: 1.417, rok: 2021
Způsob publikování: Omezený přístup
https://doi.org/10.1016/j.jmaa.2020.124523

Let T be a power bounded Hilbert space operator without unimodular eigenvalues. We show that the subsequential ergodic averages N−1∑n=1NTan converge in the strong operator topology for a wide range of sequences (an), including the integer part of most of subpolynomial Hardy functions. Moreover, we show that the weighted averages N−1∑n=1Ne2πig(n)Tan also converge for many reasonable functions g. In particular, we generalize the polynomial mean ergodic theorem for power bounded operators due to ter Elst and the second author [16] to real polynomials and polynomial weights.
Trvalý link: http://hdl.handle.net/11104/0310790