Dominated Semigroups with Singular Complex Potentials

We develop the perturbation and approximation theory for dominatedC0-semigroups onLp(1⩽p<∞) with singular complex potentials generalizing results which are known for positive semigroups with real potentials. As an application we prove nonmonotone approximation theorems for Schrödinger operators with singular magnetic fields and singular complex potentials.