### Abstract

We use recent work on spectral synthesis in multiplier algebras to give an intrinsic characterization of the separable C*-algebras A for which Orc(M(A)) = 1, i.e., for which the relation of inseparability on the topological space of primitive ideals of the multiplier algebra M(A) is an equivalence relation. This characterization has applications to the calculation of norms of inner derivations and other elementary operators on A and M(A). For example, we give necessary and sufficient conditions on the ideal structure of a separable C*-algebra A for the norm of every inner derivation to be twice the distance of the implementing element to the centre of M(A).

Original language | English |
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Pages (from-to) | 389-418 |

Number of pages | 30 |

Journal | Israel Journal of Mathematics |

Volume | 200 |

Issue number | 1 |

Early online date | 7 Feb 2014 |

DOIs | |

Publication status | Published - Jun 2014 |

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## Profiles

### Robert Archbold

- School of Natural & Computing Sciences, Mathematical Science - Emeritus Professor

Person: Honorary

## Cite this

Archbold, R. J., & Somerset, D. W. B. (2014). Separation properties in the primitive ideal space of a multiplier algebra.

*Israel Journal of Mathematics*,*200*(1), 389-418. https://doi.org/10.1007/s11856-014-0022-6