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We prove that a sectorial operator admits an H-infty - functional calculus ifand only if it has a functional model of Nagy-Foias type. Furthermore, we givea concrete formula for the characteristic function (in a generalized sense) ofsuch an operator. More generally, this approach applies to any sectorialoperator by passing to a different norm (the McIntosh square function norm). Wealso show that this quadratic norm is close to the original one, in the sensethat there is only a logarithmic gap between them.

$H^\infty$-functional calculus and models of Nagy-Foia\c{s} type for sectorial operators