Characterizations of domains of fractional powers for non-negative operators.

It is known that a closed linear operator A , defined densely on a Banach space X , is non-negative if and only if − A generates a bounded analytic γ -times resolvent family for some 0 < γ < 2 . In this paper, by using such resolvent families as well as the Komatsu representations, we characterize systematically the domains of fractional powers of non-negative operators on Banach spaces. Gaps between the subset ⋃ α > 0 D ( A α ) and the whole space X are discussed as well. [ABSTRACT FROM AUTHOR]