11 problems

Let $G$ be a locally compact group. The one-way Cowling conjecture. If $G$ is weakly amenable with $\boldsymbol\Lambda(G)=1$, then it has the Haagerup property. This is the directi…

Weak amenability conjecture for Fourier–Stieltjes algebras. The algebra $\mathrm{B}(G)$ is weakly amenable exactly when $G$ is compact with an abelian connected component of the id…

Let $\mathcal{G}$ be a Hausdorff étale groupoid. Weak amenability means that $\Lambda_{\text{cb}}(\mathcal{G})$ is finite, and the condition $\Lambda_{\text{cb}}(\mathcal{G})=1$ is…

Weak amenability conjecture. The Banach algebra $M(G)$ is weakly amenable if and only if $G$ is discrete; equivalently, zero is the only continuous point derivation of $M(G)$ at a…

Let $q\in(0,1)$, and let $h$ be the Haar weight of the little $q$-Legendre polynomial hypergroup on $\mathbb{N}_0$, given by … The associated weighted convolution algebra is…

Forrest–Runde conjecture. The Fourier algebra $\operatorname{A}(G)$ is weakly amenable if and only if the connected component of the identity in $G$ is abelian.

The 2-weak amenability conjecture. If this condition holds for every $t\in G$, then $L^1(G,\omega)$ is $2$-weakly amenable.

Let $G$ be a locally compact group, and let $G_e$ denote the connected component of the identity. Weak amenability necessity conjecture. The Fourier algebra $\mathrm{A}(G)$ can be…

Let $G$ be a compact group, and let $G_e$ denote the connected component of the identity. Forrest's conjecture. The Fourier algebra $\mathrm{A}(G)$ is weakly amenable precisely whe…

A countable group is a-T-menable if it admits a proper affine isometric action on a Hilbert space, and it has the complete metric approximation property if it is weakly amenable wi…

Let $G$ be a locally compact abelian group and let $L^1_\omega(G)$ be its Beurling algebra, where $\omega$ is a weight. Assume that … for every $t\in G$. Dales–Lau conjecture. Unde…