Partially Bounded Transformations have Trivial Centralizer
Dynamical Systems
2022-01-19 v3
Abstract
We prove that for infinite rank-one transformations satisfying a property called "partial boundedness," the only commuting transformations are powers of the original transformation. This shows that a large class of infinite measure-preserving rank-one transformations with bounded cuts have trivial centralizers. We also characterize when partially bounded transformations are isomorphic to their inverse.
Keywords
Cite
@article{arxiv.1609.04758,
title = {Partially Bounded Transformations have Trivial Centralizer},
author = {Johann Gaebler and Alexander Kastner and Cesar E. Silva and Xiaoyu Xu and Zirui Zhou},
journal= {arXiv preprint arXiv:1609.04758},
year = {2022}
}
Comments
Typos were corrected and some arguments simplified