Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.