Fractional powers of operators, ii interpolationspaces

Abstract

This is a continuation of an earlier paper “FractionalPowers of Operators” published in this Journal concerningfractional powers Aα, α∈ C, of closed linear operators A inBanach spaces X such that the resolvent (λ + A)−1 exists forall λ > 0 and λ(λ + A)−1 is uniformly hounded. Various integralrepresentations of fractional powers and relationship betweenfractional powers and interpolation spaces, due to Lions andothers, of X and domain D(Aα) are investigated. © 1967 by Pacific Journal of Mathematics.