Trace formulas for singular and additive non-selfadjoint perturbations

摘要

The paper gives an overview on trace formulas for pairs of self-adjoint, maximal dissipative and other types of resolvent comparable operators. In particular, recent results on trace formulas for singular pairs of resolvent comparable operators are presented. The results improve and generalize certain classical results of M.G. Krein for pairs of selfadjoint and dissipative operators, the results of A. Rybkin for such pairs, as well as the results of V. Adamyan, B. Pavlov, and M.G. Krein for pairs {A, A*} with a maximal dissipative operator A.