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- W1978392533 abstract "Abstract In the finite von Neumann algebra setting, we introduce the concept of a perturbation determinant associated with a pair of self-adjoint elements H 0 and H in the algebra and relate it to the concept of the de la Harpe-Skandalis homotopy invariant determinant associated with piecewise C 1-paths of operators joining H 0 and H . We obtain an analog of Krein's formula that relates the perturbation determinant and the spectral shift function and, based on this relation, we derive subsequently (i) the Birman-Solomyak formula for a general non-linear perturbation, (ii) a universality of a spectral averaging, and (iii) a generalization of the Dixmier-Fuglede-Kadison differentiation formula." @default.
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- W1978392533 date "2010-02-01" @default.
- W1978392533 modified "2023-09-30" @default.
- W1978392533 title "Some Applications of the Perturbation Determinant in Finite von Neumann Algebras" @default.
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- W1978392533 doi "https://doi.org/10.4153/cjm-2010-008-x" @default.
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