Uniform local amenability

被引：18

作者：

Brodzki, Jacek ^{[1
]}

Niblo, Graham A. ^{[1
]}

Spakula, Jan ^{[2
]}

Willett, Rufus ^{[3
]}

Wright, Nick ^{[1
]}

机构：

[1] Univ Southampton, Southampton SO17 1BJ, Hants, England

[2] Univ Munster, Math Inst, D-48149 Munster, Germany

[3] Univ Hawaii Manoa, Dept Math, Honolulu, HI 96822 USA

来源：

JOURNAL OF NONCOMMUTATIVE GEOMETRY | 2013年 / 7卷 / 02期

基金：

美国国家科学基金会; 英国工程与自然科学研究理事会;

关键词：

Coarse embedding in Hilbert space; property A; operator norm localization; metric sparsification; expander; graphs with large girth; OPERATOR NORM LOCALIZATION; GROMOV MONSTER GROUPS; HIGHER INDEX THEORY; METRIC-SPACES; LARGE GIRTH; PROPERTY; EXPANDERS; GRAPHS;

D O I：

10.4171/JNCG/128

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The main results of this paper show that various coarse ('large scale') geometric properties are closely related. In particular, we show that property 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: specifically, expanders and graphs with large girth. We also generalise and reprove a theorem of Nowak relating amenability and asymptotic dimension in the quantitative setting.

引用

页码：583 / 603

页数：21

共 50 条

[1] UNIFORM LOCAL AMENABILITY IMPLIES PROPERTY A
Elek, Gabor
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2021, 149 (06) : 2573 - 2577
[2] Characterisations for uniform amenability
Zhu, Jingming
Zhang, Jiawen
INDAGATIONES MATHEMATICAE-NEW SERIES, 2023, 34 (06): : 1318 - 1328
[3] The operator amenability of uniform algebras
Runde, V
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2003, 46 (04): : 632 - 634
[4] Amenability and uniform Roe algebras
Ara, Pere
Li, Kang
Lledo, Fernando
Wu, Jianchao
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 459 (02) : 686 - 716
[5] Uniform non-amenability
Arzhantseva, GN
Burillo, J
Lustig, M
Reeves, L
Short, H
Ventura, E
ADVANCES IN MATHEMATICS, 2005, 197 (02) : 499 - 522
[6] Regularity and amenability conditions for uniform algebras
Feinstein, J. F.
Heath, M. J.
FUNCTION SPACES, 2007, 435 : 159 - +
[7] Uniform non-amenability of free Burnside groups
Denis V. Osin
Archiv der Mathematik, 2007, 88 : 403 - 412
[8] Uniform non-amenability of free Burnside groups
Osin, Denis V.
ARCHIV DER MATHEMATIK, 2007, 88 (05) : 403 - 412
[9] Amenability and non-uniform growth of some directed automorphism groups of a rooted tree
Brieussel, Jeremie
MATHEMATISCHE ZEITSCHRIFT, 2009, 263 (02) : 265 - 293
[10] Characteristic properties and uniform non-amenability of n-periodic products of groups
Adian, S. I.
Atabekyan, V. S.
IZVESTIYA MATHEMATICS, 2015, 79 (06) : 1097 - 1110

← 1 2 3 4 5 →