Abstract
If α and α′ are one-parameter automorphism groups of a von Neumann algebraM α′ is said to be a bounded perturbation of α if ∥α′ t −α t ∥→0 ast→0. We give a complete characterization of the bounded perturbations α′ of α. In particular, we show that if α can be implemented by a strongly continuous one-parameter group with self-adjoint generator (Hamiltonian)H, then α′ can be implemented in the same way and the corresponding HamiltonianH′ can be chosen to be of the formH′=VHV −1+h, whereV is a unitary ofM andh=h*∈M.
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Communicated by H. Araki
On leave of absence from II. Institut für Theoretische Physik, Universität Hamburg, D-2000 Hamburg 50, Federal Republic of Germany
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Buchholz, D., Roberts, J.E. Bounded perturbations of dynamics. Commun.Math. Phys. 49, 161–177 (1976). https://doi.org/10.1007/BF01608739
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DOI: https://doi.org/10.1007/BF01608739