A Joint Functional Calculus for Sectorial Operators with Commuting Resolvents

Functional Calculus for Non-Commuting Operators

A Functional Calculus for Pairs of Commuting Polynomially Bounded Operators

A functional calculus valid for the class of absolutely continuous pairs of commuting polynomially bounded operators is defined.

Functional Calculus for Non-commuting Operators with Real Spectra via an Iterated Cauchy Formula

We define a smooth functional calculus for a noncommuting tuple of (unbounded) operators Aj on a Banach space with real spectra and resolvents with temperate growth, by means of an iterated Cauchy formula. The construction is also extended to tuples of more general operators allowing smooth functional calculii. We also discuss the relation to the case with commuting operators.

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 th...

The functional calculus for commuting row contractions

A commuting row contraction is a d-tuple of commuting operators T1, . . . , Td such that ∑d i=1 TiT ∗ i ≤ I. Such operators have a polynomial functional calculus which extends to a norm closed algebra of multipliers Ad on Drury-Arveson space. We characterize those row contractions which admit an extension of this map to a weak-∗ continuous functional calculus on the full multiplier algebra. In ...