Functional calculus and duality for closed operators

A new functional calculus for noncommuting operators

In this paper we use the notion of slice monogenic functions [2] to define a new functional calculus for an n-tuple T of not necessarily commuting operators. This calculus is different from the one discussed in [5] and it allows the explicit construction of the eigenvalue equation for the n-tuple T based on a new notion of spectrum for T . Our functional calculus is consistent with the Riesz-Du...

Functional Calculus for Non-Commuting Operators

The H∞−calculus and sums of closed operators

We develop a very general operator-valued functional calculus for operators with an H∞−calculus.We then apply this to the joint functional calculus of two sectorial operators when one has an H∞calculus. Using this we prove theorem of Dore-Venni type on sums of sectorial operators and apply our results to the problem of Lp−maximal regularity. Our main assumption is the R-boundedness of certain s...

Non commutative functional calculus: bounded operators

In this paper we develop a functional calculus for bounded operators defined on quaternionic Banach spaces. This calculus is based on the notion of slice-regularity, see [4], and the key tools are a new resolvent operator and a new eigenvalue problem. AMS Classification: 47A10, 47A60, 30G35.

Operators with an Absolute Functional Calculus

We study sectorial operators with a special type of functional calculus, which we term an absolute functional calculus. A typical example of such an operator is an invertible operator A (defined on a Banach space X) considered on the real interpolation space (Dom(A),X)θ,p where 0 < θ < 1 and 1 < p < ∞. In general the absolute functional calculus can be characterized in terms of real interpolati...