### Abstract

We generalize two theorems about K-automorphisms from 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.

Original language | English (US) |
---|---|

Pages (from-to) | 57-63 |

Number of pages | 7 |

Journal | Electronic Research Announcements of the American Mathematical Society |

Volume | 11 |

Issue number | 7 |

DOIs | |

State | Published - Jun 10 2005 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

}

**Spectral and mixing properties of actions of amenable groups.** / Avni, Nir.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Spectral and mixing properties of actions of amenable groups

AU - Avni, Nir

PY - 2005/6/10

Y1 - 2005/6/10

N2 - We generalize two theorems about K-automorphisms from 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.

AB - We generalize two theorems about K-automorphisms from 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.

UR - http://www.scopus.com/inward/record.url?scp=33646443969&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646443969&partnerID=8YFLogxK

U2 - 10.1090/S1079-6762-05-00147-2

DO - 10.1090/S1079-6762-05-00147-2

M3 - Article

VL - 11

SP - 57

EP - 63

JO - Electronic Research Announcements in Mathematical Sciences

JF - Electronic Research Announcements in Mathematical Sciences

SN - 1935-9179

IS - 7

ER -