2 problems

Let $\mathbb{F}$ be the free group on two generators, and let $C^*(\mathbb{F})\otimes_{\mathrm{max}}C^*(\mathbb{F})$ and $C^*(\mathbb{F})\otimes_{\mathrm{min}}C^*(\mathbb{F})$ deno…

Assume Hilbert spaces are separable with complex scalars. Let $\mathscr{X}$ be a Hilbert space, let $\rho:\mathbb{F}\times\mathbb{F}\to\mathrm{U}(\mathscr{X})$ be a unitary represe…