$H^∞$ functional calculus in real interpolation spaces
Tom 137 / 1999
Studia Mathematica 137 (1999), 161-167
DOI: 10.4064/sm-137-2-161-167
Streszczenie
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 $∥λ(λ I - A)^{-1}∥$ is bounded outside every larger sector) and has a bounded inverse, then A has a bounded $H^∞$ functional calculus in the real interpolation spaces between X and the domain of the operator itself.
