  We prove that a sectorial operator admits an H-infty - functional calculus if
and only if it has a functional model of Nagy-Foias 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.
