Abstract
For automorphism groups of operator algebras we show how properties of the difference ‖α t − α' t ‖ are reflected in relations between the generators δα, δ′α. Indeed for a von Neumann algebraM with separable predual we show that if ‖αt − α't‖ ≦ 0.28 for smallt, then δα = γ0(δ′α+δ′)°γ-1 where γ is an inner automorphism ofM and δ is a bounded derivation ofM. If the difference ‖α t − α' t ‖=O(t) ast →; 0, then δα = δ′α + δ and if ‖α t − α' t ‖ ≦ 0.28 for allt then δα=. We prove analogous results for unitary groups on a Hilbert space andC 0,C *0 groups on a Banach space.
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Communicated by J. Glimm
This paper subsumes an earlier work of the same title which appeared as a report from Z.I.F. der Universität Bielefeld
With partial support of the U.S. National Science Foundation
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Bratteli, O., Herman, R.H. & Robinson, D.W. Perturbations of flows on Banach spaces and operator algebras. Commun.Math. Phys. 59, 167–196 (1978). https://doi.org/10.1007/BF01614248
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DOI: https://doi.org/10.1007/BF01614248