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Uniform local amenability

Uniform local amenability
Uniform local amenability
The main results of this paper show that various coarse (‘large scale’) geometric properties are closely related. In particular, we show that prop- erty A implies the operator norm localisation property, and thus that norms of operators associated to a very large class of metric spaces can be effectively estimated.
The main tool is a new property called uniform local amenability. This property is easy to negate, which we use to study some ‘bad’ spaces. We also generalise and reprove a theorem of Nowak relating amenability and asymptotic dimension in the quantitative setting.
amenability, metric sparsification, operator norm localisation, non commutative geometry, geometric group theory, Yu's property A, coarse embeddability
1661-6952
583-603
Brodzki, Jacek
b1fe25fd-5451-4fd0-b24b-c59b75710543
Niblo, Graham
43fe9561-c483-4cdf-bee5-0de388b78944
Špakula, Ján
c43164e4-36a7-4372-9ce2-9bfbba775d77
Willett, Rufus
9f00bf4a-53ab-47b5-9f59-d12174765907
Wright, Nick
f4685b8d-7496-47dc-95f0-aba3f70fbccd
Brodzki, Jacek
b1fe25fd-5451-4fd0-b24b-c59b75710543
Niblo, Graham
43fe9561-c483-4cdf-bee5-0de388b78944
Špakula, Ján
c43164e4-36a7-4372-9ce2-9bfbba775d77
Willett, Rufus
9f00bf4a-53ab-47b5-9f59-d12174765907
Wright, Nick
f4685b8d-7496-47dc-95f0-aba3f70fbccd

Brodzki, Jacek, Niblo, Graham, Špakula, Ján, Willett, Rufus and Wright, Nick (2013) Uniform local amenability. Journal of Noncommutative Geometry, 7 (2), 583-603. (doi:10.4171/JNCG/128).

Record type: Article

Abstract

The main results of this paper show that various coarse (‘large scale’) geometric properties are closely related. In particular, we show that prop- erty A implies the operator norm localisation property, and thus that norms of operators associated to a very large class of metric spaces can be effectively estimated.
The main tool is a new property called uniform local amenability. This property is easy to negate, which we use to study some ‘bad’ spaces. We also generalise and reprove a theorem of Nowak relating amenability and asymptotic dimension in the quantitative setting.

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e-pub ahead of print date: 29 March 2012
Published date: 7 May 2013
Keywords: amenability, metric sparsification, operator norm localisation, non commutative geometry, geometric group theory, Yu's property A, coarse embeddability
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 336622
URI: https://eprints.soton.ac.uk/id/eprint/336622
ISSN: 1661-6952
PURE UUID: 8378aa1a-0868-4205-822d-8de3e6dd58fc
ORCID for Graham Niblo: ORCID iD orcid.org/0000-0003-0648-7027
ORCID for Ján Špakula: ORCID iD orcid.org/0000-0001-5775-9905
ORCID for Nick Wright: ORCID iD orcid.org/0000-0003-4884-2576

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Date deposited: 02 Apr 2012 15:18
Last modified: 15 Aug 2019 00:55

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