Related papers: An example of a non-amenable dynamical system whic…

We study skew-amenable topological groups, i.e., those admitting a left-invariant mean on the space of bounded real-valued functions left-uniformly continuous in the sense of Bourbaki. We prove characterizations of skew-amenability for…

Let $UC(K)$ denote the Banach space of all bounded uniformly continuous functions on a hypergroup $K$. The main results of this article concern on the $\alpha$-amenability of $UC(K)$ and quotients and products of hypergroups. It is also…

We prove that for any non-zero, countable ordinal $\xi$ which is not additively indecomposable, the property of having Szlenk index not exceeding $\omega^\xi$ is not a three space property. This complements a result of Brooker and Lancien,…

We show that the universal minimimal proximal flow and the universal minimal strongly proximal flow of a discrete group can be realized as the Stone spaces of translation invariant Boolean algebras of subsets of the group satisfying a…

We consider the amenability of groupoids $G$ equipped with a group valued cocycle $c:G\to Q$ with amenable kernel $c^{-1}(e)$. We prove a general result which implies, in particular, that $G$ is amenable whenever $Q$ is amenable and if…

Third-order ordinary differential equations with Lie symmetry algebras isomorphic to the nonsolvable algebra $\mathfrak{sl}(2,\mathbb{R})$ admit solvable structures. These solvable structures can be constructed by using the basis elements…

We show that the group of bounded automatic automorphisms of a rooted tree is amenable, which implies amenability of numerous classes of groups generated by finite automata. The proof is based on reducing the problem to showing amenability…

We prove a version of ergodic theorem for an action of an amenable group, where a F{\o} lner sequence needs not to be tempered. Instead, it is assumed that a function satisfies certain mixing condition.

Let Gamma be a finitely generated, amenable group. Using an idea of E Ghys, we prove that if Gamma has a nontrivial, orientation-preserving action on the real line, then Gamma has an infinite, cyclic quotient. (The converse is obvious.)…

We give a necessary and sufficient condition for amenability of the Banach algebra of approximable operators on a Banach space. We further investigate the relationship between amenability of this algebra and factorization of operators,…

Let $\mathbb{G}$ be a compact quantum group and $A\subseteq B$ an inclusion of $\sigma$-finite $\mathbb{G}$-dynamical von Neumann algebras. We prove that the $\mathbb{G}$-inclusion $A\subseteq B$ is strongly equivariantly amenable if and…

We observe that a Polish group $G$ is amenable if and only if every continuous action of $G$ on the Hilbert cube admits an invariant probability measure. This generalizes a result of Bogatyi and Fedorchuk. We also show that actions on the…

We give lower bounds for the electrical resistance between vertices in the Schreier graphs of the action of the linear (degree 1) and quadratic (degree 2) mother groups on the orbit of the zero ray. These bounds, combined with results of…

In this article we construct examples of non-smoothable $\mathbb{Z}/p$-actions on indefinite spin 4-manifolds with boundary for all primes $p\geq 5$. For example, we show that for each prime $p\geq 5$ and each $n\geq 1$ there exists a…

In this paper we prove that if (A,\pi) is an amenable Banach algebra and if \rho is another Banach algebra multiplication on A such that the difference between \rho and and \pi is less than 1/11, then (A, \rho) is also amenable.

Runde and Spronk showed in 2004 that there are non-amenable groups $G$, including $\mathbb F_2$, {whose Fourier-Stieltjes algebra, $B(G)$,} is operator Connes-amenable. This result was surprising since the measure algebra $M(G)$ is…

We extend the concept of amenability of a Banach algebra $A$ to the case that there is an extra $\mathfrak A$-module structure on $A$, and show that when $S$ is an inverse semigroup with subsemigroup $E$ of idempotents, then $A=\ell^1(S)$…

We prove that the alternating group of a topologically free action of a countably infinite group $\Gamma$ on the Cantor set has the property that all of its $\ell^2$-Betti numbers vanish and, in the case that $\Gamma$ is amenable, is stable…

Using ultrapowers of $C^{\ast}$-algebras we provide a new construction of the multiplier algebra of a $C^{\ast}$-algebra. This extends the work of Avsec and Goldbring [Houston J. Math., to appear, arXiv:1610.09276.] to the setting of…

This paper recalls a partial differential equations system, which is the linearization of a recognized fluid-elasticity interaction three-dimensional model. A collection of regularity results for the traces of the fluid variable on the…