Higher-order trace formulas for contractive and dissipative operators

Abstract We establish higher-order trace formulas for pairs of contractions along a multiplicative path generated by a self-adjoint operator in a Schatten-von Neumann ideal, removing earlier stringent restrictions on the kernel and defect operator of the contractions and significantly enlarging the set of admissible functions. We also derive higher-order trace formulas for maximal dissipative operators under relaxed assumptions and new simplified trace formulas for unitary and resolvent comparable self-adjoint operators. The respective spectral shift measures are absolutely continuous and, in the case of contractions, the set of admissible functions for the n th-order trace formula on the unit circle includes the Besov class $B^n_{\infty , 1}(\mathbb {T})$ . Both aforementioned properties are new in the mentioned generality.