Partially Bounded Transformations have Trivial Centralizers

Johann Gaebler, Alexander Kastner, Cesar Silva, Xiaoyu Xu, and Zirui Zhou

Proceedings of the American Mathematical Society, 2018.

ArXiv: 1609.04758.

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.