4 problems

Weak amenability–Haagerup conjecture. A group is weakly amenable with constant $1$ if and only if it has the Haagerup property.

Let $G$ be a countable group. An approximate representation is a sequence of maps $\phi_n\colon G\to\mathcal U(n)$ that is asymptotically multiplicative, and it is separating when…

Failure conjecture. The converse implication fails: there exists a maximal operator space that is not strongly maximal, owing to the lack of a suitable approximation property in…

Cohen-forcing conjecture. If $W\subset V$ satisfies the $\kappa$-cover and approximation properties, then forcing with ${\rm Add}(\kappa,1)^V$ does not add a generic for…