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

Generation of analytic semigroups on Banach space X by − ( A + k B ) 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 k ∈ C is a parameter satisfying Re k > c for some c ∈ R . 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 L p ( R N ) is discussed.