5 problems

Figà-Talamanca–Picardello conjecture. $A_r(G)$ is dense in $B_0(G)$, equivalently

Let $G$ be a locally compact group. Write $\widetilde{\mathrm{A}}(G)_1$ for the unit ball of the unitization of the Fourier algebra $\mathrm{A}(G)$, let $\mathcal{C}_0(G)$ denote t…

Let $G$ be a locally compact group, and let $\tau_\rho$ denote the representation associated with a representation $\rho$. A representation $\rho$ is spectrally natural when…

Let $G$ and $H$ be locally compact groups. Suppose that $G$ is amenable, and let $\Phi:{\mathrm{A}(G)}\to{\mathrm{B}(H)}$ be a bounded homomorphism. A continuous map…

Let $G$ be a locally compact group and let ${\mathrm{A}(G)}$ denote its Fourier algebra. Operator biflatness conjecture. ${\mathrm{A}(G)}$ is always operator biflat. This would ext…