Trace formulas for relative Schatten class perturbations

We derive trace formulas for a pair of self-adjoint operators H+V and H under the assumption that (H−i)−1V is in a Schatten class. This extends the trace formulas of [8], where V alone is assumed to be in a Schatten class. Our trace formulas apply, in particular, in the setting of differential operators and are based on Taylor-like approximations of operator functions. This significantly improves non-Taylor based trace formulas of [10].