A Katznelson-Tzafriri type theorem for Ces\`aro bounded operators
Functional Analysis
2016-05-25 v3
Abstract
We extend the well-known Katznelson-Tzafriri theorem, originally posed for power-bounded operators, to the case of Ces\`aro bounded operators of any order For this purpose, we use a functional calculus between a new class of fractional Wiener algebras and the algebra of bounded linear operators, whose existence is characterized by the Ces\`aro boundedness. Finally, we apply the main theorem to get ergodicity results for the Ces\`aro means of bounded operators.
Cite
@article{arxiv.1506.06609,
title = {A Katznelson-Tzafriri type theorem for Ces\`aro bounded operators},
author = {Luciano Abadias},
journal= {arXiv preprint arXiv:1506.06609},
year = {2016}
}