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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
Article

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 andC0,C 0 * groups on a Banach space.

Keywords

Neural Network Statistical Physic Hilbert Space Banach Space Complex System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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