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A Krengel-type theorem for finitely-generated nilpotent groups

Published online by Cambridge University Press:  02 October 2001

V. BERGELSON ,
I. KORNFELD ,
A. LEIBMAN  and
B. MITYAGIN
V. BERGELSON
Affiliation:
Ohio State University, Columbus, OH 43210, USA (e-mail: {vitaly,leibman,borismit}@math.ohio-state.edu)
I. KORNFELD
Affiliation:
North Dakota State University, Fargo, ND 58105, USA (e-mail: kornfeld@plains.nodak.edu)
A. LEIBMAN
Affiliation:
Ohio State University, Columbus, OH 43210, USA (e-mail: {vitaly,leibman,borismit}@math.ohio-state.edu)
B. MITYAGIN
Affiliation:
Ohio State University, Columbus, OH 43210, USA (e-mail: {vitaly,leibman,borismit}@math.ohio-state.edu)
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Abstract

Let \{U_{g}\}_{g\in G} be a weakly mixing unitary action of a finitely-generated nilpotent group on a Hilbert space \mathcal{H}. Extending a known result about abelian groups, we show that weakly wandering vectors are dense in \mathcal{H}.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 5 , October 2001 , pp. 1359 - 1369
Copyright
2001 Cambridge University Press

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