Related papers: Bekka-type amenabilities for unitary corepresentat…

Let $A$ be a Banach algebra with a non-empty character space. We say that a bounded net $\{e_{\alpha}\}$ in $A$ is a bounded $\Delta$-weak approximate identity for $A$ if, for each $a\in A$ and compact subset $K$ of $\Delta(A)$,…

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…

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.…

In this paper we first show that for a locally compact amenable group $G$, every proper abstract Segal algebra of the Fourier algebra on $G$ is not approximately amenable; consequently, every proper Segal algebra on a locally compact…

Let $L^1_\om(G)$ be a Beurling algebra on a locally compact abelian group $G$. We look for general conditions on the weight which allows the vanishing of continuous derivations of $L^1_\om(G)$. This leads us to introducing vector-valued…

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 a weak form of the mean ergodic theorem for actions of amenable locally compact quantum groups in the von Neumann algebra setting.

We prove that the following are equivalent for a locally compact group $G$: (i) $G$ is amenable; (ii) $M(G)$ is Connes-amenable; (iii) $M(G)$ has a normal, virtual diagonal.

Let $A$ be a Banach algebra and $A^{**}$ be the second dual of it. We show that by some new conditions, $A$ is weakly amenable whenever $A^{**}$ is weakly amenable. We will study this problem under generalization, that is, if $(n+2)-th$…

Let $K$ be a commutative hypergroup and $\alpha\in \hat{K}$. We show that $K$ is $\alpha$-amenable with the unique $\alpha$-mean $m_\alpha$ if and only if $m_\alpha\in L^1(K)\cap L^2(K)$ and $\alpha$ is isolated in $\hat{K}$. In contrast to…

For a topological group $G$, amenability can be characterized by the amenability of the convolution Banach algebra $L^1(G)$. Here a Banach algebra $A$ is called amenable if every bounded derivation from $A$ into any dual--type…

We give a partial solution to a long-standing open problem in the theory of quantum groups, namely we prove that all finite-dimensional representations of a wide class of locally compact quantum groups factor through matrix quantum groups…

We show that an \'etale groupoid which is strongly amenable at infinity is amenable whenever its full and reduced $C^*$-algebras coincide.

Let $A$ be a Banach algebra and $A^{**}$ be the second dual of it. We show that by some new conditions, $A$ is weakly amenable whenever $A^{**}$ is weakly amenable. We will study this problem under generalization, that is, if $(n+2)-th$…

We define a Banach algebra A to be dual if $A = (A_\ast)^\ast$ for a closed submodule $A_\ast$ of $A^\ast$. The class of dual Banach algebras includes all $W^\ast$-algebras, but also all algebras M(G) for locally compact groups G, all…

Let $G$ and $H$ be locally compact, second countable groups. Assume that $G$ acts in a measure class preserving way on a standard probability space $(X,\mu)$ such that $L^\infty(X,\mu)$ has an invariant mean and that there is a Borel…

A well-known theorem of Day and Dixmier states that any uniformly bounded representation of an amenable locally compact group $G$ on a Hilbert space is similar to a unitary representation. Within the category of locally compact quantum…

Let G be a compact connected Lie group. We prove that the Fourier algebra A(G) is weakly amenable if and only if G is abelian.

For locally compact groups amenability and Kazhdan's property (T) are mutually exclusive in the sense that a group having both properties is compact. This is no longer true for more general Polish groups. However, a weaker result still…

For second countable discrete quantum groups, and more generally second countable locally compact quantum groups with trivial scaling group, we show that property (T) is equivalent to every weakly mixing unitary representation not having…