Operator integrals, spectral shift and spectral flow

Details Operator integrals, spectral shift and spectral flow Operator integrals, spectral shift and spectral flow

2007-03-14

arxiv.org/abs/math/0703442v1

Mathematics

Operator Algebras

To appear in Canadian Journal of Mathematics

Scientific paper

We present a new and simple approach to the theory of multiple operator integrals that applies to unbounded operators affiliated with general von Neumann algebras. For semifinite von Neumann algebras we give applications to the Fr\'echet differentiation of operator functions that sharpen existing results, and establish the Birman-Solomyak representation of the spectral shift function of M.G. Krein in terms of an average of spectral measures in the type II setting. We also exhibit a surprising connection between the spectral shift function and spectral flow.

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