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

Abstract

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.

26 pages

Cited by in corpus (1)

• On measuring unboundedness of the $H^{\infty }$-calculus for generators of analytic semigroups