2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78000We introduce the concept of a spectral shift operator and use it to derive Krein's spectral shift function for pairs of self-adjoint operators. Our principal tools are operator-valued Herglotz functions and their logarithms. Applications to Krein's trace formula and to the Birman-Solomyak spectral averaging formula are discussed.LaTeX, 28 pagesSpectral Theorytext