On weakly mixing and doubly ergodic nonsingular actions

• Autorzy: Sarah Iams , Brian Katz , Cesar E. Silva , Brian Street , Kirsten Wickelgren
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37A40: Nonsingular (and infinite-measure preserving) transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2005
• Tom: 103
• Numer: 2
• Strony: 247-264

Daty

wydano

2005

Twórcy

autor

Sarah Iams

• Williams College, Williamstown, MA 01267, U.S.A.
• Emmanuel College, Cambridge, CB2 3AP, UK

autor

Brian Katz

• Williams College, Williamstown, MA 01267, U.S.A.
• Department of Mathematics, University of Texas Austin, TX 78712, U.S.A.

autor

Cesar E. Silva

• Department of Mathematics, Williams College, Williamstown, MA 01267, U.S.A.

autor

Brian Street

• University of Virginia, Charlottesville, VA 22903, U.S.A.
• Department of Mathematics, Princeton University, Princeton, NJ 08544, U.S.A.

autor

Kirsten Wickelgren

• Harvard University, Cambridge, MA 02138, U.S.A.
• Department of Mathematics, Stanford University, Palo Alto, CA 94305, U.S.A.

Identyfikatory

DOI

10.4064/cm103-2-10