Commutators, C0-semigroups and resolvent estimates

Abstract We study the existence and the continuity properties of the boundary values on the real axis of the resolvent of a self-adjoint operator H in the framework of the conjugate operator method initiated by Mourre. We allow the conjugate operator A to be the generator of a C 0 -semigroup (finer estimates require A to be maximal symmetric) and we consider situations where the first commutator [ H ,i A ] is not comparable to H . The applications include the spectral theory of zero mass quantum field models.