Questions tagged [amenability]
The amenability tag has no summary.
168 questions
6
votes
1
answer
249
views
Means on WAP(S) with S a cancellative left amenable semigroup
$\DeclareMathOperator\WAP{WAP}$Question: Suppose that $S$ is a discrete cancellative left amenable semigroup and $m$ is a left invariant mean on $\ell^\infty(S)$. When we restrict $m$ to $\WAP(S)$, ...
- 103
4
votes
0
answers
200
views
Passage of amenability, and the Følner condition to corners of von Neumann Algebras
Let $(M,\tau)$ be a tracial von Neumann algebra, and $q \in M$ be a (nonzero) projection, and let $\mathcal H = L^2(M)$ be the standard representation.
Using the definition of injectivity ($M \subset ...
- 407
1
vote
0
answers
240
views
Collect characterizations of amenability of group as many as possible
My hobby is to collect characterizations of amenability of group as many as possible. If the accumulation amounts to 365, then I'm planning to make a day-by-day calendar which deals with one of them ...
2
votes
0
answers
170
views
Why a discrete amenable group satisfy Følner condition?
A discrete group $G$ satisfying Følner condition means that there exists a net $(F_j)_{j\in J}$ of nonempty finite subsets of $G$ such that $\mathop{lim}\limits_{j}\frac{|F_j\triangle gF_j|}{|F_j|}=0$ ...
- 99
4
votes
0
answers
74
views
Reflexive symmetrically amenable Banach algebra
It is a 33 yrs. old conjecture that amenable Banach algebras that are reflexive as Banach spaces are finite dimensional [1]. To the best of my knowledge, there is no proof of this conjecture in this ...
- 2,988
12
votes
2
answers
749
views
Group with a translation invariant ultrafilter
Let $G$ be an infinite, discrete, countable group. Can $G$ have a translation-invariant ultrafilter? An ultrafilter $\mathcal{F} \subset 2^G$ is translation-invariant if $A \in \mathcal{F}$ implies $g ...
- 1,332
2
votes
0
answers
135
views
Amenability and the unitary group of an operator algebra
Let $M$ be a von Neumann algebra and $U(M)=\{x\in M: x^*=x^{-1}\}$ be its unitary group. In this post, we equip $U(M)$ only with the relative weak$^*$ topology $\sigma(M,M_*)$. Then, $U(M)$ is a ...
- 2,988
3
votes
1
answer
268
views
Can we find background noise for every Følner sequence in a countable amenable group?
Let $G$ be a countable amenable group. We consider sequences $(z_g)_{g\in G}$ of complex numbers with $|z_g|=1$ for all $g\in G$.
I will say $(z_g)_{g\in G}$ is background noise for a (left-)Følner ...
- 13.1k
5
votes
0
answers
167
views
Non-monotileable amenable groups
This is crossposted from MSE.
We say a subset $A$ of a group $G$ is a monotile for $G$ if $G$ is a disjoint union of right translates of $A$.
In his article Monotileable Amenable Groups, B. Weiss ...
- 13.1k
1
vote
0
answers
284
views
Does every amenable group $G$ admit a two-sided Folner sequence?
By two-sided Følner sequence I mean a sequence $(F_N)_N$ of subsets of $G$ which is both a left-Følner and a right-Følner sequence.
Context: I just came up with this question and surprisingly I haven'...
- 13.1k
0
votes
0
answers
135
views
Amenability of $\textrm{w}_0(A)$ for a $C^*$-algebra $A$
Let $A$ be a $C^*$-algebra with only finite dimensional irreducible representations. As in a previous question, let $\textrm{w}_0(A)$ denote the subspace of $\ell^{\infty}(A)$ consisting of all weakly ...
- 2,988
1
vote
0
answers
147
views
Amenability of $\textrm{w}_0(L^1(G))$
Let $G$ be an infinite compact group and $A=L^1(G)$. It is known that $c_0(A)$ is amenable [Runde2020, p.80] while $\ell^{\infty}(A)$ is not [Daws2009] .
Let $\textrm{w}_0(A)$ denote the subspace of $\...
- 2,988
3
votes
1
answer
211
views
Topological amenability of actions - forgetting topology
Let $G$ be a (countable) discrete group and let $X$ be a locally compact Hausdorff space.
Assume that $G$ acts on $X$ by homeomorphisms. Recall that the action is (topologically) amenable if there ...
- 536
15
votes
1
answer
1k
views
Is the infinite product of solvable groups amenable?
I am interested in the amenability properties of infinite products of solvable groups. The following facts are well-known:
Any solvable group is amenable.
The class of solvable groups is closed under ...
- 153
1
vote
1
answer
243
views
Nonamenable p.m.p. action on a standard probability space
Let $G$ be a discrete nonamenable countable group acting on a standard probability space $(X,\mu)$ through measure-preserving transformations.
Is the action of $G$ always amenable?
(Amenable action, ...
- 133