Asymptotic limits, Banach limits, and Ces\`aro means
Functional Analysis
2020-10-29 v1
Abstract
Every new inner product in a Hilbert space is obtained from the original one by means of a unique positive operator The first part of the paper is a survey on applications of such a technique, including a characterization of similarity to isometries The second part focuses on Banach limits for dealing with power bounded operators. It is shown that if a power bounded operator for which the sequence of shifted Ces\`aro means converges (at least in the weak topology) uniformly in the shift parameter, then it has a Ces\`aro asymptotic limit coinciding with its -asymptotic limit for all Banach limits .
Cite
@article{arxiv.2010.14740,
title = {Asymptotic limits, Banach limits, and Ces\`aro means},
author = {C. S. Kubrusly and B. P. Duggal},
journal= {arXiv preprint arXiv:2010.14740},
year = {2020}
}