Accepted author manuscript, 120 KB, PDF document
Available under license: CC BY-NC-ND: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
Accepted author manuscript
Licence: CC BY-NC-ND: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Uniform Local Amenability implies Property A
AU - Elek, Gabor
PY - 2021/3/18
Y1 - 2021/3/18
N2 - In this short note we answer a query of Brodzki, Niblo, \v{S}pakula, Willett and Wright \cite{ULA} by showing thatall bounded degree uniformly locally amenable graphs have Property A. For the second result of the noterecall that Kaiser \cite{Kaiser} proved that if $\Gamma$ is a finitely generated group and $\{H_i\}^\infty_{i=1}$ isa Farber sequence of finite index subgroups, then the associated Schreier graph sequence is of Property A if and only if the group is amenable.We show however, that there exist a non-amenable group and a nested sequence of finite index subgroups $\{H_i\}^\infty_{i=1}$ such that$\cap H_i=\{e_\Gamma\}$, and the associated Schreier graph sequence is of Property A.
AB - In this short note we answer a query of Brodzki, Niblo, \v{S}pakula, Willett and Wright \cite{ULA} by showing thatall bounded degree uniformly locally amenable graphs have Property A. For the second result of the noterecall that Kaiser \cite{Kaiser} proved that if $\Gamma$ is a finitely generated group and $\{H_i\}^\infty_{i=1}$ isa Farber sequence of finite index subgroups, then the associated Schreier graph sequence is of Property A if and only if the group is amenable.We show however, that there exist a non-amenable group and a nested sequence of finite index subgroups $\{H_i\}^\infty_{i=1}$ such that$\cap H_i=\{e_\Gamma\}$, and the associated Schreier graph sequence is of Property A.
U2 - 10.1090/proc/15387
DO - 10.1090/proc/15387
M3 - Journal article
VL - 149
SP - 2573
EP - 2577
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
ER -