A class of relatively bounded perturbations for generators of bounded analytic semigroups in Banach spaces.

Abstract: Generation of analytic semigroups on Banach space X by is shown, where A is a negative generator of a bounded analytic semigroup on X, B is a closed operator in X belonging to a class related to A and is a parameter satisfying for some . The proof may be regarded as a modification of the perturbation argument established by Okazawa [8]. As applications, the generation of non-contractive analytic semigroups by Schrödinger operators with inverse square potentials in is discussed. [Copyright &y& Elsevier]