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+kB) 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 Rek>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 Lp(RN) is discussed.