Power bounded operators and the mean ergodic theorem for subsequences

Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00532219" target="_blank" >RIV/67985840:_____/21:00532219 - isvavai.cz</a>
Výsledek na webu
<a href="https://doi.org/10.1016/j.jmaa.2020.124523" target="_blank" >https://doi.org/10.1016/j.jmaa.2020.124523</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2020.124523" target="_blank" >10.1016/j.jmaa.2020.124523</a>

Jazyk výsledku
angličtina
Název v původním jazyce
Power bounded operators and the mean ergodic theorem for subsequences
Popis výsledku v původním jazyce
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.
Název v anglickém jazyce
Power bounded operators and the mean ergodic theorem for subsequences
Popis výsledku anglicky
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.

Projekt
<a href="/cs/project/GX20-31529X" target="_blank" >GX20-31529X: Abstraktní konvergenční schémata a jejich složitost</a><br>
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění
2021
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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