4 problems

Let $\mathcal{A}$ be an exact C$^\ast$-algebra, and let $I(\mathcal{A})$ denote its injective envelope. Ozawa's conjecture. There is a nuclear C$^\ast$-algebra $N(\mathcal{A})$ suc…

Let $0\to I\to E\to B\to 0$ be an asymptotically split extension of NF algebras, meaning that the quotient map admits an asymptotic completely positive contractive splitting. Brown…

Nuclearity conjecture. ${\mathcal{C}}$ is nuclear if and only if ${\mathcal{A}}$ is nuclear.

Let $\mathcal{B}$ be a Fell bundle, and let $C^*_{\mathrm{r}}(\mathcal{B})$ denote its reduced cross-sectional $C^*$-algebra. Araújo–Exel–Katsura's conjecture. Nuclearity of…