Trace formulas for additive and non-additive perturbations

We improve and generalize certain classical results of M.G. Kreĭn for pairs of self-adjoint and dissipative operators, results of A.V. Rybkin for such pairs as well as of V.M. Adamjan, B.S. Pavlov and M.G. Kreĭn for pairs {H,H⁎} with a maximal dissipative operator H.