9 problems

Operator amenability characterization conjecture. The Fourier–Stieltjes algebra $\mathrm{B}(G)$ is operator amenable if and only if

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 $\mathrm{G}(\mathbb{Q})$ be an algebraic group admitting an embedding of $\mathbb{Q}$, and let $\mathrm{G}(\mathbb{Q}_p)$ and $\mathrm{G}(\mathbb{R})$ denote its groups of poin…

Converse conjecture for $B(G)$. If $B(G)$ has a normal, virtual diagonal, then $G$ has an abelian subgroup of finite index; moreover, the same converse should hold with the existen…

Let $G$ be a locally compact group, let $G_d$ denote the same group with the discrete topology, and let $B(G)$ and $B(G_d)$ be their Fourier–Stieltjes algebras. Define the discreti…

Lau–Loy conjecture. To capture the amenability of $G$ through an amenability condition on $B(G)$ or $B_r(G)$, the condition must take into account both the operator-space structure…

Compactness conjecture. Either of these algebras is operator amenable if and only if $G$ is compact.

Let $G$ be a locally compact unimodular group. Let $E^2$ denote the $G$-invariant ideal considered above, namely the subspace of Fourier–Stieltjes functions in $L^2(G)$, with the o…

Let $G$ be a locally compact group, and let $vn(G)=\ell^\infty\text{-}\bigoplus_{\pi\in\hat{G}}\mathcal{B}(\mathcal{H}_\pi)$ be the von Neumann algebra dual of $a(G)$. The spine id…