Some results about complex powers of closed operators (Q748830)

The authors establish a number of results concerning linear operators on a complex Banach space having bounded imaginary powers. In particular, they provide an estimate of the state of decrease at infinity of the resolvent of a positive operator with bounded imaginary powers. They also give a sufficient condition for a perturbation of positive operators with bounded imaginary powers to have bounded imaginary powers and a related result on the growth of the imaginary powers of the sum of two operators satisfying certain conditions.