3 problems

Integer-valued similarity-degree conjecture. The value of $d(A)$ can be any integer.

Infinite-degree conjecture. There exists a $C^*$-algebra $A$ such that

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…