Perturbation theory for commutative m-tuples of self-adjoint operators

AbstractGeneralizing the Weyl-von Neumann theorem for normal operators, we show that a commutative m-tuple of self-adjoint operators in a separable Hilbert space may be changed into a diagonal one by adding compact perturbations of class cp, for p>m. On the other hand it is shown that the absolutely continuous part, defined appropriately, of a commutative m-tuple of self-adjoint operators is stable under perturbations of class cp, if p < m, m ⩾ 3, or if p = 1, m = 2 (the latter case m = 2 corresponding to the case of one normal operator). For the proof of these Kato-Rosenblum-type theorems a wave operator method for m-tuples is introduced