On operators with bounded imaginary powers in Banach spaces (Q1116066)

Closed linear densely defined operators A in a Banach space X are considered which admit bounded imaginary powers. A functional calculus for such operators is presented which in particular shows that \(\epsilon +A\) has again this property, with the same bounds. This is the basis for our extension of the Dore-Venni theorem to operators which may not be invertible but have zero kernels. The main results are then applied to an abstract Volterra equation in a \(\zeta\)-convex Banach space which arises in the mathematical theory of viscoelasticity.