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
583-603
Brodzki, Jacek
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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
7 May 2013
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), .
(doi:10.4171/JNCG/128).
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
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Local EPrints ID: 336622
URI: http://eprints.soton.ac.uk/id/eprint/336622
ISSN: 1661-6952
PURE UUID: 8378aa1a-0868-4205-822d-8de3e6dd58fc
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Date deposited: 02 Apr 2012 15:18
Last modified: 15 Mar 2024 03:48
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Author:
Rufus Willett
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