2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78300The recently introduced concept of a spectral shift operator is applied in several instances. Explicit applications include Krein's trace formula for pairs of self-adjoint operators, the Birman-Solomyak spectral averaging formula and its operator-valued extension, and an abstract approach to trace formulas based on perturbation theory and the theory of self-adjoint extensions of symmetric operators.LaTeX, 27 pagesSpectral Theorytext