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Spectral and mixing properties of actions of amenable groups

Author(s): Nir Avni
Journal: Electron. Res. Announc. Amer. Math. Soc. 11 (2005), 57-63.
MSC (2000): Primary 37A15; Secondary 37A20
Posted: June 10, 2005
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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: 10.1090/S1079-6762-05-00147-2
PII: S 1079-6762(05)00147-2
Received by editor(s): May 27, 2004
Posted: June 10, 2005
Communicated by: Klaus Schmidt
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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