$H^{∞}$ functional calculus in real interpolation spaces, II
LetA be a linear closed one-to-one operator in a complex Banach spaceX, having dense domain and dense range. IfA is of type! (i.e. the spectrum ofA is contained in a sector of angle 2!, symmetric about the real positive axis, and k (I A) 1 k is bounded outside every larger sector), then A has a bounded H 1 functional calculus in the real interpolation spaces between X and the intersection of the domain and the range of the operator itself.