Perturbation Formulas for Traces on Normed Ideals

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 s...

Full description

Saved in:

Bibliographic Details
Published in:	Communications in mathematical physics Vol. 325; no. 3; pp. 1107 - 1138
Main Authors:	Dykema, Ken, Skripka, Anna
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01-02-2014
Subjects:	Classical and Quantum Gravitation Complex Systems Mathematical and Computational Physics Mathematical Physics Physics Physics and Astronomy Quantum Physics Relativity Theory Theoretical Trace Class Noncommutative Geometry Spectral Shift Normed Ideal Trace Formula
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	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.
ISSN:	0010-3616 1432-0916
DOI:	10.1007/s00220-013-1828-5