Fritz Gesztesy, Konstantin A. Makarov, and Serguei N. Naboko
The Spectral Shift Operator
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ABSTRACT. We 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.