  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.
