Perturbation formulas for traces on normed ideals
Functional Analysis
2015-06-12 v3 Operator Algebras
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.
Cite
@article{arxiv.1211.0776,
title = {Perturbation formulas for traces on normed ideals},
author = {Ken Dykema and Anna Skripka},
journal= {arXiv preprint arXiv:1211.0776},
year = {2015}
}
Comments
33 pages, typos corrected; to appear in Comm. Math. Phys