2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153989We introduce a relative index for a pair of dissipative operators in a von Neumann algebra of finite type and prove an analog of the Birman-Schwinger principle in this setting. As an application of this result, revisiting the Birman-Krein formula in the abstract scattering theory, we represent the de la Harpe-Skandalis determinant of the characteristic function of dissipative operators in the algebra in terms of the relative index.Spectral TheoryMathematical PhysicsOperator Algebras47A55; 47C15; 47A53text