Perturbation formulas for traces on normed ideals

Abstract

We prove perturbation results for traces on normed ideals in semifinite von Neumann algebra factors. This includes the case of Dixmier traces. In particular, we establish existence of spectral shift measures with initial operators being dissipative or bounded, and show that these measures can have singular components in the case of Dixmier traces. We also establish a linearization formula for a Dixmier trace applied to perturbed operator functions, a result that does not typically hold for normal traces.

33 pages, typos corrected; to appear in Comm. Math. Phys

References in corpus (3)

• Dixmier traces and some applications to noncommutative geometry
• Higher order spectral shift for contractions
• The spectral shift function and spectral flow

Cited by in corpus (1)

• Second order trace formulae