Communications in Mathematical Physics

, Volume 59, Issue 2, pp 167–196 | Cite as

Perturbations of flows on Banach spaces and operator algebras

  • Ola Bratteli
  • Richard H. Herman
  • Derek W. Robinson


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 andC0,C 0 * groups on a Banach space.


Neural Network Statistical Physic Hilbert Space Banach Space Complex System 
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Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Ola Bratteli
    • 1
  • Richard H. Herman
    • 1
  • Derek W. Robinson
    • 1
  1. 1.Department of MathematicsPennsylvania State UniversityUniversity ParkUSA

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