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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Spectral rigidity of group actions: Applications to the case gr$ \langle t,s ; ts=st^2\rangle$


Author: Oleg N. Ageev
Journal: Proc. Amer. Math. Soc. 134 (2006), 1331-1338
MSC (2000): Primary 37A05, 37A15, 37A25, 37A30, 37A35, 28D05, 28D15; Secondary 47A05, 47A35, 47D03
Published electronically: October 6, 2005
MathSciNet review: 2199176
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Abstract | References | Similar Articles | Additional Information

Abstract: We apply a technique to study the notion of spectral rigidity of group actions to a group gr$ \langle t,s ; ts=st^2\rangle$. As an application, we prove that there exist rank one weakly mixing transformations conjugate to its square, thereby giving a positive answer to a well-known question.


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Additional Information

Oleg N. Ageev
Affiliation: Department of Mathematics, Moscow State Technical University, 2nd Baumanscaya St. 5, 105005 Moscow, Russia
Address at time of publication: Max Planck Institute of Mathematics, P.O. Box 7280, D-53072 Bonn, Germany
Email: ageev@mx.bmstu.ru, ageev@mpim-bonn.mpg.de

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08380-2
PII: S 0002-9939(05)08380-2
Keywords: Group actions, ergodic theory, conjugations to its squares
Received by editor(s): November 20, 2004
Published electronically: October 6, 2005
Additional Notes: The author was supported in part by the Max Planck Institute of Mathematics, Bonn, and the Programme of Support of Leading Scientific Schools of the RF (grant no. NSh-457.2003.1)
Communicated by: Michael Handel
Article copyright: © Copyright 2005 American Mathematical Society