Mean ergodic composition operators in spaces of homogeneous polynomials
Functional Analysis
2020-12-16 v1
Abstract
We study some dynamical properties of composition operators defined on the space of -homogeneous polynomials on a Banach space when is endowed with two different topologies: the one of uniform convergence on compact sets and the one defined by the usual norm. The situation is quite different for both topologies: while in the case of uniform convergence on compact sets every power bounded composition operator is uniformly mean ergodic, for the topology of the norm there is no relation between the latter properties. Several examples are given.
Cite
@article{arxiv.1909.03743,
title = {Mean ergodic composition operators in spaces of homogeneous polynomials},
author = {David Jornet and Daniel Santacreu and Pablo Sevilla-Peris},
journal= {arXiv preprint arXiv:1909.03743},
year = {2020}
}