%0 Journal Article
%T Poisson-Pinsker factor and infinite measure preserving group actions
%A Emmanuel Roy
%J Mathematics
%D 2009
%I arXiv
%X We solve the question of the existence of a Poisson-Pinsker factor for conservative ergodic infinite measure preserving action of a countable amenable group by proving the following dichotomy: either it has totally positive Poisson entropy (and is of zero type), or it possesses a Poisson-Pinsker factor. If G is abelian and the entropy positive, the spectrum is absolutely continuous (Lebesgue countable if G=\mathbb{Z}) on the whole L^{2}-space in the first case and in the orthocomplement of the L^{2}-space of the Poisson-Pinsker factor in the second.
%U http://arxiv.org/abs/0909.1425v1