The distance formula for the derivation problem (Q308223)

The author considers a type II factor \(\mathcal{M}\) on a separable Hilbert space and shows that the distance between a given operator \(x\in\mathcal{M}\) and the commutant \(\mathcal{M}'\) equals the distance between \(x\) and the center \(\mathbb{C}I\) of \(\mathcal{M}\). This implies that the norm of the derivation induced by \(x\) equals the distance from \(x\) to \(\mathcal{M}'\).