Partially bounded transformations have trivial centralizers

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

doi:10.1090/proc/14091

Partially bounded transformations have trivial centralizers
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by Johann Gaebler, Alexander Kastner, Cesar E. Silva, Xiaoyu Xu and Zirui Zhou

Proc. Amer. Math. Soc. 146 (2018), 5113-5127

DOI: https://doi.org/10.1090/proc/14091

Published electronically: September 17, 2018

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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.

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