On multiplicative perturbation of integral resolvent families

In this paper we study multiplicative perturbations for the generator of a strongly continuous integral resolvent family of bounded linear operators defined on a Banach space X. Assuming that a(t) is a creep function which satisfies a(0+) > 0, we prove that if (A, a) generates an integral resolvent, then (A(I + B),a) also generates an integral resolvent for all B ∈ B(X,Z), where Z belongs to a class of admissible Banach spaces. In special instances of a(t) the space Z is proved to be characterized by an extended class of Favard spaces. © 2006 Elsevier Inc. All rights reserved.