Perturbations of flows on Banach spaces and operator algebras

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

Research output: Contribution to journalArticle

Abstract

For automorphism groups of operator algebras we show how properties of the difference {norm of matrix}αt - α't{norm of matrix} are reflected in relations between the generators δα, δ′α. Indeed for a von Neumann algebra M with separable predual we show that if {norm of matrix}αt - α't{norm of matrix} ≦ 0.28 for small t, then δα = γ0(δ′α+δ′)°γ-1 where γ is an inner automorphism of M and δ is a bounded derivation of M. If the difference {norm of matrix}αt - α't{norm of matrix}=O(t) as t →; 0, then δα = δ′α + δ and if {norm of matrix}αt - α't{norm of matrix} ≦ 0.28 for all t then δα=. We prove analogous results for unitary groups on a Hilbert space and C0, C0* groups on a Banach space.

Original languageEnglish (US)
Pages (from-to)167-196
Number of pages30
JournalCommunications in Mathematical Physics
Volume59
Issue number2
DOIs
StatePublished - Jun 1 1978

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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