## Ergodicity and conservativity of products of infinite transformations and their inverses

### Volume 143 / 2016

Colloquium Mathematicum 143 (2016), 271-291
MSC: Primary 37A40; Secondary 37A05, 37A50.
DOI: 10.4064/cm6482-10-2015
Published online: 17 February 2016

#### Abstract

We construct a class of rank-one infinite measure-preserving transformations such that for each transformation $T$ in the class, the cartesian product $T\times T$ 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.