Diagonalization modulo a class of Orlicz ideals

We consider a class of norm ideals CG which are non-commutative analogues of Orlicz spaces and which satisfy a previously introduced condition called (QK). We give a spectral condition which is necessary and sufficient for a commuting tuple of self-adjoint operators A = (A1, . . . , An) to be simultaneously diagonalizable modulo CG. © 2006 Elsevier Inc. All rights reserved.