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arXiv · 1609.04758

Partially Bounded Transformations have Trivial Centralizer

Johann Gaebler·Alexander Kastner·Cesar E. Silva·Xiaoyu Xu·Zirui Zhou
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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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Johann Gaebler, Alexander Kastner, Cesar E. Silva, Xiaoyu Xu, Zirui Zhou. 2016-09-15. Partially Bounded Transformations have Trivial Centralizer. https://arxiv.org/abs/1609.04758

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