### Abstract

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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### Cite this

*Israel Journal of Mathematics*,

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

**Separation properties in the primitive ideal space of a multiplier algebra.** / Archbold, Robert J; Somerset, Douglas W. B.

Research output: Contribution to journal › Article

*Israel Journal of Mathematics*, vol. 200, no. 1, pp. 389-418. https://doi.org/10.1007/s11856-014-0022-6

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TY - JOUR

T1 - Separation properties in the primitive ideal space of a multiplier algebra

AU - Archbold, Robert J

AU - Somerset, Douglas W. B.

PY - 2014/6

Y1 - 2014/6

N2 - 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).

AB - 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).

U2 - 10.1007/s11856-014-0022-6

DO - 10.1007/s11856-014-0022-6

M3 - Article

VL - 200

SP - 389

EP - 418

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

IS - 1

ER -