Related papers: Amenability properties of Rajchman algebras

For a locally compact Abelian group $G$, the algebra of Rajchman measures, denoted by $M_0(G)$, is the set of all bounded regular Borel measures on $G$ whose Fourier transform vanish at infinity. In this paper, we investigate the spectral…

Let G be a locally compact group, and let A(G) and B(G) denote its Fourier and Fourier-Stieltjes algebras. These algebras are dual objects of the group and measure algebras, L^1(G) and M(G), in a sense which generalizes the Pontryagin…

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,…

A topological group $G$ is called extremely amenable if every continuous action of $G$ on a compact space has a fixed point. This concept is linked with geometry of high dimensions (concentration of measure). We show that a von Neumann…

For a locally compact group $G$, let $A(G)$ denote its Fourier algebra, $M_{cb}(A(G))$ the completely bounded multipliers of $A(G)$, and $A_{M_cb}(G)$ the closure of $A(G)$ in $M_{cb}(A(G))$. We show that, if $A_{M_cb}(G)$ is amenable, then…

We study amenability of affine algebras (based on the notion of almost-invariant finite-dimensional subspace), and apply it to algebras associated with finitely generated groups. We show that a group G is amenable if and only if its group…

In 1972, B. E. Johnson proved that a locally compact group $G$ is amenable if and only if certain Hochschild cohomology groups of its convolution algebra $L^1(G)$ vanish. Similarly, $G$ is compact if and only if $L^1(G)$ is biprojective: In…

A topological group $G$ is extremely amenable if every continuous action of $G$ on a compact space has a fixed point. Using the concentration of measure techniques developed by Gromov and Milman, we prove that the group of automorphisms of…

We give for a compact group G, a full characterisation of when its Fourier algebra A(G) is weakly amenable: when the connected component of the identity G_e is abelian. This condition is also equivalent to the hyper-Tauberian property for…

We consider the Fourier-Stietljes algebra B(G) of a locally compact group G. We show that operator amenablility of B(G) implies that a certain semitolpological compactification of G admits only finitely many idempotents. In the case that G…

Let $G$ be a locally compact group, and let $B(G)$ denote its Fourier--Stieltjes algebra. We show that $B(G)$ is Connes-amenable if and only if $G$ is almost abelian.

We study locally compact groups for which the Fourier algebra coincides with the Rajchman algebra. In particular, we show that there exist uncountably many non-compact groups with this property. Generalizing a result of Hewitt 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.…

We show that if a locally compact group $G$ is non-abelian then the amenability constant of its Fourier algebra is $\geq 3/2$, extending a result of Johnson (JLMS, 1994) who proved that this holds for finite non-abelian groups. Our lower…

Let A be a Banach algebra and I be a closed ideal of A. We say that A is amenable relative to I, if A/I is an amenable Banach algebra. We study the relative amenability of Banach algebras and investigate the relative amenability of…

We let the central Fourier algebra, ZA(G), be the subalgebra of functions u in the Fourier algebra A(G) of a compact group, for which u(xyx^{-1})=u(y) for all x,y in G. We show that this algebra admits bounded point derivations whenever G…

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 an example of a non-compact, locally compact group $G$ such that its Fourier-Stieltjes algebra $B(G)$ is operator amenable. Furthermore, we characterize those $G$ for which $A^*(G)$ - the spine of $B(G)$ as introduced by M. Ilie and…

We study the closed algebra B_I(G) generated by the idempotents in the Fourier-Stieltjes algebra of a locally compact group G. We show that it is a regular Banach algebra with computable spectrum G^I, which we call the idempotent…

The notion of operator amenability was introduced by Z.-J. Ruan in 1995. He showed that a locally compact group G is amenable if and only if its Fourier algebra A(G) is operator amenable. In this paper, we investigate the operator…