Operators with an absolute functional calculus
Skip to main content
Open Access Publications from the University of California


UCLA Previously Published Works bannerUCLA

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 interpolation spaces. We show that operators of this type have a strong form of the H ∞-calculus and behave very well with respect to the joint functional calculus. We give applications of these results to recent work of Arendt, Batty and Bu on the existence of Hölder-continuous solutions for the abstract Cauchy problem.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
For improved accessibility of PDF content, download the file to your device.
Current View