Related papers: Reiter's properties (P_1) and (P_2) for locally co…

If $H$ is a lattice in a locally compact second countable group $G$, then we show that $G$ has property A (respectively is coarsely embeddable into Hilbert space) if and only if $H$ has property A (respectively is coarsely embeddable into…

We show that the amenability of a locally compact group $G$ is equivalent to a factorization property of $VN(G)$ which is given by $ VN(G) = <VN(G)^*VN(G)>$. This answer partially two problems proposed by Z. Hu and M. Neufang in their…

We study weak amenability for locally compact quantum groups in the sense of Kustermans and Vaes. In particular, we focus on non-discrete examples. We prove that a coamenable quantum group is weakly amenable if there exists a net of…

Let G be a locally compact group, and let 1 < p < \infty. In this paper we investigate the injectivity of the left L^1(G)-module L^p(G). We define a family of amenability type conditions called (p,q)-amenability, for any 1 <= p <= q. For a…

The Haagerup property for locally compact groups is generalised to the context of locally compact quantum groups, with several equivalent characterisations in terms of the unitary representations and positive-definite functions established.…

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…

Let G be a locally compact group, and ZL1(G) be the centre of its group algebra. We show that when $G$ is compact ZL1(G) is not amenable when G is either nonabelian and connected, or is a product of infinitely many finite nonabelian groups.…

A locally compact group $G$ is called Hermitian if the spectrum $\text{Sp}_{L^1(G)}(f)\subseteq\mathbb R$ for every $f\in L^1(G)$ satisfying $f=f^*$, and called quasi-Hermitian if $\text{Sp}_{L^1(G)}(f)\subseteq\mathbb R$ for every $f\in…

Let $K$ be a commutative compact hypergroup and $L^1(K)$ the hypergroup algebra. We show that $L^1(K)$ is amenable if and only if $\pi_K$, the Plancherel weight on the dual space $\widehat{K}$, is bounded. Furthermore, we show that if $K$…

We prove that the $L^1$-algebra of any non-Kac type compact quantum group does not satisfy operator biflatness. Since operator amenability implies operator biflatness, this result shows that any co-amenable, non-Kac type compact quantum…

Let $G$ be a locally compact group. We show that its Fourier algebra $A(G)$ is amenable if and only if $G$ has an abelian subgroup of finite index, and that its Fourier-Stieltjes algebra $B(G)$ is amenable if and only if $G$ has a compact,…

For a locally compact quantum group $\mathbb{G}$, the quantum group algebra $L^1(\mathbb{G})$ is operator amenable if and only if it has an operator bounded approximate diagonal. It is known that if $L^1(\mathbb{G})$ is operator biflat and…

In this short note we answer a query of Brodzki, Niblo, \v{S}pakula, Willett and Wright by showing that all bounded degree uniformly locally amenable graphs have Property A. For the second result of the note recall that Kaiser proved that…

Let $A_p(G)$ denote the Figa-Talamanca-Herz Banach Algebra of the locally compact group $G$, thus $A_2(G)$ is the Fourier Algebra of $G$. If $G$ is commutative then $A_2(G)=L^1(\hat{G}){\hat{}}$. Let $A^r_p(G)=A_p\cap L^r(G)$ with norm…

It is shown that a locally compact group $G$ is amenable if and only if some certain closed ideals of the Fig\`{a}-Talamanca-Herz algebra $A_{p}(G)$ admit bounded $\Delta$-weak approximate identities. Also, similar results are obtained for…

A locally compact groupoid is said to have the weak containment property if its full $C^*$-algebra coincides with its reduced one. This property is strictly weaker than amenability and is known to be equivalent to amenability for…

We study the concept of co-amenability for a compact quantum group. Several conditions are derived that are shown to be equivalent to it. Some consequences of co-amenability that we obtain are faithfulness of the Haar integral and automatic…

We prove that the measure algebra $M(G)$ of a locally compact group $G$ is Connes-amenable if and only if $G$ is amenable.

We prove that a compact quantum group is coamenable if and only if its corepresentation ring is amenable. We further propose a Foelner condition for compact quantum groups and prove it to be equivalent to coamenability. Using this Foelner…

A common fixed point property for semigroups is applied to show that the group algebra $L^1(G)$ of a locally compact group $G$ is $2m$-weakly amenable for each integer $m\geq 1$.