English

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

R2 v1 2026-06-22T15:51:02.719Z