8 problems

Sauvageot-product triviality conjecture. The Sauvageot product with respect to the embedding is isomorphic to $B$:

Let ${\mathcal{S}}$ denote the set of completely positive trace-preserving maps on ${\mathcal{M}}_2$, and let $T_2$ be the partial trace over the second factor. For a unitary matri…

Let $\mathfrak{A}$ be a unital $C^{\star}$-algebra, and let $T$ be a completely positive linear map on $\mathfrak{A}$ such that $T(1)=1$. Write … for the spectrum of $T$, and let ……

Let $\Phi:{\mathfrak A}\to{\mathfrak A}$ be a unital completely positive map acting on the unital $C^*$-algebra ${\mathfrak A}$, and let $\sigma(\Phi)$ denote its spectrum. Periphe…

Let $\mathcal{G}$ and $\mathcal{H}$ be Hilbert spaces, let $\mathcal{B}(\mathcal{G})$ and $\mathcal{B}(\mathcal{H})$ denote the corresponding type $I$ factors, and let a normal UCP…

Extremality conjecture. The function $k_1^\mathrm{WYD}$ is an extreme point of $\mathcal{K}^+$. The function lies on the boundary of $\mathcal{K}^+$; the conjecture concerns whethe…

Let $k$ be a positive integer and let $T_1,\ldots,T_k$ be a commuting $k$-tuple of unital completely positive maps on a von Neumann algebra. A strong dilation is an E-dilation…

Non-recurrent-point range conjecture. If $\boxed{\textstyle\text{?}}$ is non-recurrent, then