Operator Integrals, Spectral Shift, and Spectral Flow

By Nurulla Azamov, Alan L. Carey, P. Dodds, Fedor Sukochev. Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2007

109 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ca1c76eb78df908c0445007dd421ebe4684be3b3

Citations in the corpus

• Multiple operator integrals in perturbation theory (2015, unknown): “The following proof is based on the approach of [14].”