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 | References | Similar Articles | Additional Information

Abstract: We generalize two theorems about K-automorphisms from 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

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.