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## Spectral and mixing properties of actions of amenable groups

### Nir Avni

**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.

*Copyright 2005 American Mathematical Society
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#### Article Info

- ERA Amer. Math. Soc.
**11** (2005), pp. 57-63
- Publisher Identifier: S 1079-6762(05)00147-2
- 2000
*Mathematics Subject Classification*. Primary 37A15; Secondary 37A20
- Received by editors May 27, 2004
- Posted on June 10, 2005
- Communicated by Klaus Schmidt
- Comments (When Available)

**Nir Avni**

Department of Mathematics, Hebrew University of Jerusalem, Israel

*E-mail address:* `anir@math.huji.ac.il`

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