3 problems

Solel's conjecture. The same result should hold even when $\Phi$ is not weak-continuous. The paper constructs a unital, completely positive, idempotent $L^{\infty}(\mathbb{T})$-bim…

Commutator-ideal conjecture. The kernels of $R_1$ and $R_2$ should both equal the closed commutator ideal of $CB_{d4d5}(B(d4d4))$.

Functional-calculus conjecture. It should be possible to extend this functional calculus beyond the w-continuous module maps to a homomorphism from all of $CB_{d4d5}(B(d4d4))$ into…