Operator Integrals, Spectral Shift, and Spectral Flow
Nurulla AzamovAzamov, Dodds) School of Computer Science, Engineering and Mathematics, Flinders University of South Australia, Bedford Park, 5042, SA, AustraliaAlan L. CareyFlinders UniversityPeter G. DoddsCarey)Mathematical Sciences Institute, Australian National University, Canberra, ACT 0200, AustraliaFedor SukochevSukochev) School of Mathematics and Statistics, University of New South Wales, Kensington, NSW 2052, Australia
2009en
ABI
Annotatsiya
Abstract. 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 Fréchet 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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