5 problems

Clouâtre–Ostermann–Ransford conjecture. (i) If $\|\Lambda\|\leq 2$, then $\|\theta\|\leq 2$. (ii) If $\alpha$ is a complete contraction, $\theta$ is completely bounded, and…

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 $M$ be a finite von Neumann algebra and let $N$ be a semifinite von Neumann algebra. Suppose $1{\leqslant} p<\infty$ with $p\ne 2$, and let … be an isometry with a Yeadon facto…

Let $M$ be a finite von Neumann algebra and let $N$ be a semifinite von Neumann algebra. Suppose $1{\leqslant} p<\infty$ with $p\ne 2$, and let … be a not necessarily surjective is…

Type-invariance conjecture. The same type-invariance for radial multipliers that holds for free Araki-Woods factors should hold for all $q$-Araki-Woods algebras.