  We prove an analogue of the Lebesgue decomposition for continuous functionals
on the commutant modulo a reflexive normed ideal of an n-tuple of hermitian
operators for which there are quasicentral approximate units relative to the
normed ideal. Using results of Godefroy-Talagrand and Pfitzner we derive from
this strong uniqueness of the predual of such a commutant modulo a normed
ideal.
