4 problems

Let $\mathbb{F}_\infty$ be the free group with countably infinitely many generators, and let $C^*(\mathbb{F}_\infty)$ be its full group $C^*$-algebra. A $C^*$-algebra has the weak…

Let $n\geq 3$, and let $\ell_1^n$ be the $n$-dimensional operator space. A finite-dimensional operator space is controllable when it satisfies the controllability property defined…

Let $\ell_1^3$ be the three-dimensional operator space and let $M_k(\ell_1^3)$ denote its $k\times k$ matrix amplification. Say that an operator space is controllable when it has t…

Let $\mathscr{C}=C^*(\mathbb{F}_\infty)$, and let a finite-dimensional operator subspace $E\subset\mathscr{C}$ be controllable when it is completely isometric to a subspace having…