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IP-rigidity and eigenvalue groups

Published online by Cambridge University Press:  08 March 2013

JON AARONSON ,
MARYAM HOSSEINI  and
MARIUSZ LEMAŃCZYK
JON AARONSON
Affiliation:
School of Mathematical Sciences, Tel Aviv University, 69978 Tel Aviv, Israel email [email protected]
MARYAM HOSSEINI
Affiliation:
Department of Mathematics and Statistics, University of Ottawa, 585 King Edward, Ottawa, ON, K1N 6N5, Canada email [email protected]
MARIUSZ LEMAŃCZYK
Affiliation:
Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland email [email protected]
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Abstract

We examine the class of increasing sequences of natural numbers which are IP-rigidity sequences for some weakly mixing probability-preserving transformation. This property is closely related to the uncountability of the eigenvalue group of a corresponding non-singular transformation. We give examples, including a super-lacunary sequence which is not IP-rigid.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 34 , Issue 4 , August 2014 , pp. 1057 - 1076
Copyright
Copyright ©2013 Cambridge University Press 

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