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 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm6482-10-2015,
author = {Julien Clancy and Rina Friedberg and Indraneel Kasmalkar and Isaac Loh and Tudor P\u adurariu and Cesar E. Silva and Sahana Vasudevan},
title = {Ergodicity and conservativity of products of infinite transformations and their inverses},
journal = {Colloquium Mathematicae},
volume = {144},
year = {2016},
pages = {271-291},
zbl = {06574987},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6482-10-2015}
}
Julien Clancy; Rina Friedberg; Indraneel Kasmalkar; Isaac Loh; Tudor Pădurariu; Cesar E. Silva; Sahana Vasudevan. Ergodicity and conservativity of products of infinite transformations and their inverses. Colloquium Mathematicae, Tome 144 (2016) pp. 271-291. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6482-10-2015/