Bounded perturbations of dynamics

If alpha and alpha ' are one-parameter automorphism groups of a von Neumann algebra M, alpha ' is said to be a bounded perturbation of alpha if // alpha /sub t/'- alpha /sub t/// to O at t to O. The authors give a complete characterization of the bounded perturbations alpha ' of alpha . In particular, they show that if alpha can be implemented by a strongly continuous one-parameter group with self- adjoint generator (Hamiltonian) H, then alpha ' can be implemented in the same way and the corresponding Hamiltonian H' can be chosen to be of the form H'-VHV/sup -1/+h, where V is a unitary of M and h=h* epsilon M. (16 refs).