\(H ^{\infty }\)-functional calculus and models of Nagy-Foiaş type for sectorial operators (Q652240)

The authors prove that a sectorial operator admits an \(H^{\infty}\)-functional calculus if and only if it has a functional model of Nagy-Foiaş type. Furthermore, they give a concrete formula for the characteristic function of such an operator. More generally, this approach applies to any sectorial operator by passing to a different norm (the McIntosh square function norm). They also show that this quadratic norm is close to the original one, in the sense that there is only a logarithmic gap between them.