We study weak mixing and double ergodicity for nonsingular actions of locally compact Polish abelian groups. We show that if T is a nonsingular action of G, then T is weakly mixing if and only if for all cocompact subgroups A of G the action of T restricted to A is weakly mixing. We show that a doubly ergodic nonsingular action is weakly mixing and construct an infinite measure-preserving flow that is weakly mixing but not doubly ergodic. We also construct an infinite measure-preserving flow whose cartesian square is ergodic.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-2-10,
author = {Sarah Iams and Brian Katz and Cesar E. Silva and Brian Street and Kirsten Wickelgren},
title = {On weakly mixing and doubly ergodic nonsingular actions},
journal = {Colloquium Mathematicae},
volume = {103},
year = {2005},
pages = {247-264},
zbl = {1083.37007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-2-10}
}
Sarah Iams; Brian Katz; Cesar E. Silva; Brian Street; Kirsten Wickelgren. On weakly mixing and doubly ergodic nonsingular actions. Colloquium Mathematicae, Tome 103 (2005) pp. 247-264. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-2-10/