COMPLEX POWERS OF OPERATORS

Abstract

We define the complex powers of a densely defined operator A whose resolvent exists in a suitable region of the complex plane. Generally, this region is strictly contained in an angle and there exists α ∈ (0, ∞ )s uch that the resolvent of A is bounded by O((1 + |λ|) α ) there. We prove that for some particular choices of a fractional number b, the negative of the fractional power (−A) b is the c.i.g. of an analytic semigroup of growth order r> 0.