Uniform local amenability implies Property A

نویسندگان

چکیده

In this short note we answer a query of Brodzki, Niblo, \v{S}pakula, Willett and Wright \cite{ULA} by showing that all bounded degree uniformly locally amenable graphs have Property A. For the second result recall Kaiser \cite{Kaiser} proved if $\Gamma$ is finitely generated group $\{H_i\}^\infty_{i=1}$ Farber sequence finite index subgroups, then associated Schreier graph A only amenable. We show however, there exist non-amenable nested subgroups such $\cap H_i=\{e_\Gamma\}$,

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Amenability and the Liouville Property

We present a new approach to the amenability of groupoids (both in the measure theoretical and the topological setups) based on using Markov operators. We introduce the notion of an invariant Markov operator on a groupoid and show that the Liouville property (absence of non-trivial bounded harmonic functions) for such an operator implies amenability of the groupoid. Moreover, the groupoid actio...

متن کامل

THE WEAK-A∞ PROPERTY OF HARMONIC AND p-HARMONIC MEASURES IMPLIES UNIFORM RECTIFIABILITY

Let E ⊂ Rn+1, n ≥ 2, be an Ahlfors-David regular set of dimension n. We show that the weak-A∞ property of harmonic measure, for the open set Ω := Rn+1 \ E, implies uniform rectifiability of E. More generally, we establish a similar result for the Riesz measure, p-harmonic measure, associated to the p-Laplace operator, 1 < p < ∞.

متن کامل

Pointwise Hyperbolicity Implies Uniform Hyperbolicity

We provide a general mechanism for obtaining uniform information from pointwise data. A sample result is that if a diffeomorphism of a compact Riemannian manifold has pointwise expanding and contracting continuous invariant cone families, then the diffeomorphism is an Anosov diffeomorphism, i.e., the entire manifold is uniformly hyperbolic.

متن کامل

The operator amenability of uniform algebras

We prove a quantized version of a theorem by M. V. Shĕınberg: A uniform algebra equipped with its canonical, i.e. minimal, operator space structure is operator amenable if and only if it is a commutative C∗-algebra.

متن کامل

Uniform Non–amenability of Free Burnside Groups

The aim of the present note is to show that free Burnside groups of sufficiently large odd exponent are non–amenable in a certain strong sense, more precisely, their left regular representations are isolated from the trivial representation uniformly on finite generating sets. This result is applied to the solution of a strong version of the von Neumann – Day problem concerning amenability of gr...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Proceedings of the American Mathematical Society

سال: 2021

ISSN: ['2330-1511']

DOI: https://doi.org/10.1090/proc/15387