Partially Bounded Transformations have Trivial Centralizer

TL;DR

This paper proves that infinite rank-one transformations with partial boundedness have trivial centralizers, meaning their only commuting transformations are their powers, and characterizes when they are isomorphic to their inverses.

Contribution

It establishes the triviality of centralizers for a broad class of infinite measure-preserving rank-one transformations with partial boundedness.

Findings

Transformations with partial boundedness have trivial centralizers.

Characterization of when these transformations are isomorphic to their inverses.

Large class of bounded rank-one transformations with trivial centralizers.

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.