3 problems

Nelson's trick conjecture. There should be a Nelson's trick type argument in $2$ variables.

Let $A\subset B(\mathcal H)$ be a unital operator algebra. Let $\theta:A\to M_n(\mathbb{C})$ be a unital completely bounded homomorphism, and let $\alpha:A\to A$ be a unital antili…

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…