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ISSN 1079-6762

 

Spectral and mixing properties of actions of amenable groups


Author: Nir Avni
Journal: Electron. Res. Announc. Amer. Math. Soc. 11 (2005), 57-63
MSC (2000): Primary 37A15; Secondary 37A20
Published electronically: June 10, 2005
MathSciNet review: 2150945
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Abstract: We generalize two theorems about K-automorphisms from $\mathbb{Z} $ to all amenable groups with good entropy theory (this class includes all unimodular amenable groups which are not an increasing union of compact subgroups). The first theorem is that such actions are uniformly mixing; the second is that their spectrum is Lebesgue with countable multiplicity. For the proof we will develop an entropy theory for discrete amenable equivalence relations.


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Additional Information

Nir Avni
Affiliation: Department of Mathematics, Hebrew University of Jerusalem, Israel
Email: anir@math.huji.ac.il

DOI: http://dx.doi.org/10.1090/S1079-6762-05-00147-2
PII: S 1079-6762(05)00147-2
Received by editor(s): May 27, 2004
Published electronically: June 10, 2005
Communicated by: Klaus Schmidt
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.