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Operator Integrals, Spectral Shift, and Spectral Flow |
Canad. J. Math. 61(2009), 241-263
Published:2009-04-01
Printed: Apr 2009
Printed: Apr 2009
- N. A. Azamov
- A. L. Carey
- P. G. Dodds
- F. A. Sukochev
Abstract
We present a new and simple approach to the theory of multiple
operator integrals that applies to unbounded operators affiliated with general \vNa s.
For semifinite \vNa s 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.
| MSC Classifications: |
47A56 - Functions whose values are linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones) 47B49 - Transformers, preservers (operators on spaces of operators) 47A55 - Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15] 46L51 - Noncommutative measure and integration |