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On weakly mixing and doubly ergodic nonsingular actions

Tom 103 / 2005

Colloquium Mathematicum 103 (2005), 247-264 MSC: Primary 37A40. DOI: 10.4064/cm103-2-10

Streszczenie

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.

Autorzy

• Sarah IamsWilliams College
Williamstown, MA 01267, U.S.A.
and
Emmanuel College
Cambridge, CB2 3AP, UK
e-mail
• Brian KatzWilliams College
Williamstown, MA 01267, U.S.A.
and
Department of Mathematics
University of Texas Austin, TX 78712, U.S.A.
e-mail
• Cesar E. SilvaDepartment of Mathematics
Williams College
Williamstown, MA 01267, U.S.A.
e-mail
• Brian StreetUniversity of Virginia
Charlottesville, VA 22903, U.S.A.
and
Department of Mathematics
Princeton University
Princeton, NJ 08544, U.S.A.
e-mail
• Kirsten WickelgrenHarvard University
Cambridge, MA 02138, U.S.A.
and
Department of Mathematics
Stanford University
Palo Alto, CA 94305, U.S.A.
e-mail

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