H-functional Calculus and Models of Nagy-foiaş Type for Sectorial Operators

We prove that a sectorial operator admits an H∞functional calculus if and only if it has a functional model of NagyFoiaş type. Furthermore, we give a concrete formula for the characteristic function (in a generalized sense) of such an operator. More generally, this approach applies to any sectorial operator by passing to a different norm (the McIntosh square function norm). We also show that this quadratic norm is close to the original one, in the sense that there is only a logarithmic gap between them. M.S.C.(2000): Primary: 47A45; Secondary: 47A60, 32A10.