Trace formulas for resolvent comparable operators

We derive trace formulas for self-adjoint perturbations of self-adjoint operators such that the difference of the resolvents of the initial and perturbed operators is an element of a Schatten–von Neumann ideal SnSn, n∈Nn∈N. This substantially extends the result of [11] for perturbations corresponding to the resolvent difference in the Hilbert–Schmidt class S2S2 and the result of [13] for perturbations in SnSn, n∈Nn∈N.