### Abstract

For automorphism groups of operator algebras we show how properties of the difference {norm of matrix}α_{t} - α'_{t}{norm of matrix} are reflected in relations between the generators δ_{α}, δ′_{α}. Indeed for a von Neumann algebra M with separable predual we show that if {norm of matrix}α_{t} - α'_{t}{norm of matrix} ≦ 0.28 for small t, then δ_{α} = 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}α_{t} - α'_{t}{norm of matrix}=O(t) as t →; 0, then δ_{α} = δ′_{α} + δ and if {norm of matrix}α_{t} - α'_{t}{norm of matrix} ≦ 0.28 for all t then δ_{α}=. We prove analogous results for unitary groups on a Hilbert space and C_{0}, C_{0}^{*} groups on a Banach space.

Original language | English (US) |
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Pages (from-to) | 167-196 |

Number of pages | 30 |

Journal | Communications in Mathematical Physics |

Volume | 59 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1 1978 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

*Communications in Mathematical Physics*,

*59*(2), 167-196. https://doi.org/10.1007/BF01614248