functional calculus in real interpolation spaces
Let A be a linear closed densely defined operator in a complex Banach space X. If A is of type ω (i.e. the spectrum of A is contained in a sector of angle 2ω, symmetric around the real positive axis, and is bounded outside every larger sector) and has a bounded inverse, then A has a bounded functional calculus in the real interpolation spaces between X and the domain of the operator itself.