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Ergodicity and conservativity of products of infinite transformations and their inverses

Julien Clancy; Rina Friedberg; Indraneel Kasmalkar; Isaac Loh; Tudor Pădurariu; Cesar E. Silva; Sahana Vasudevan — 2016

Colloquium Mathematicae

We construct a class of rank-one infinite measure-preserving transformations such that for each transformation T in the class, the cartesian product T × T is ergodic, but the product $T \times T^{- 1}$ is not. We also prove that the product of any rank-one transformation with its inverse is conservative, while there are infinite measure-preserving conservative ergodic Markov shifts whose product with their inverse is not conservative.

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