Spectral and mixing properties of actions of amenable groups

Nir Avni*

*Corresponding author for this work

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)57-63
Number of pages7
JournalElectronic Research Announcements of the American Mathematical Society
Volume11
Issue number7
DOIs
StatePublished - Jun 10 2005

Fingerprint

Amenable Group
Entropy
Henri Léon Lebésgue
Equivalence relation
Theorem
Countable
Automorphisms
Multiplicity
Union
Subgroup
Generalise
Class

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

@article{fd3d0c08516743c3a23e92f288dc8dfe,
title = "Spectral and mixing properties of actions of amenable groups",
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.",
author = "Nir Avni",
year = "2005",
month = "6",
day = "10",
doi = "10.1090/S1079-6762-05-00147-2",
language = "English (US)",
volume = "11",
pages = "57--63",
journal = "Electronic Research Announcements in Mathematical Sciences",
issn = "1935-9179",
publisher = "American Mathematical Society",
number = "7",

}

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

In: Electronic Research Announcements of the American Mathematical Society, Vol. 11, No. 7, 10.06.2005, p. 57-63.

Research output: Contribution to journalArticle

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 -