### Abstract

Let A be a stable, sigma-unital, continuous C-0(X)-algebra with surjective base map phi : Prim(A) -> X, where Prim(A) is the primitive ideal space of the C*-algebra A. Suppose that phi(-1) (x) is contained in a limit set in Prim(A) for each x is an element of X (so that A is quasi-standard). Let C-R(X) be the ring of continuous real-valued functions on X. It is shown that there is a homeomorphism between the space of minimal prime ideals of C-R(X) and the space MinPrimal(M(A)) of minimal closed primal ideals of the multiplier algebra M(A). If A is separable then MinPrimal(M(A)) is compact and extremally disconnected but if X = beta N \ N then MinPrimal(M(A)) is nowhere locally compact.

Original language | English |
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Title of host publication | Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics |

Editors | Wolfgang Arendt, Ralph Chill, Yuri Tomilov |

Publisher | Springer |

Pages | 17-29 |

Number of pages | 13 |

ISBN (Electronic) | 978-3-319-18494-4 |

ISBN (Print) | 978-3-319-18493-7 |

DOIs | |

Publication status | Published - 2015 |

Event | Conference on Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics - Herrenhut, Germany Duration: 1 Jun 2013 → … |

### Publication series

Name | Operator Theory: Advances and Applications |
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Publisher | Birkhäuser Basel |

Volume | 250 |

ISSN (Print) | 0255-0156 |

ISSN (Electronic) | 0255-0156 |

### Conference

Conference | Conference on Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics |
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Country | Germany |

City | Herrenhut |

Period | 1/06/13 → … |

### Fingerprint

### Keywords

- C∗-algebra
- C0(X)-algebra
- multiplier algebra
- minimal prime ideal
- minimal primal ideal
- primitive ideal space
- quasi standard

### Cite this

_{0}(

*X*)-algebra. In W. Arendt, R. Chill, & Y. Tomilov (Eds.),

*Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics*(pp. 17-29). (Operator Theory: Advances and Applications; Vol. 250). Springer . https://doi.org/10.1007/978-3-319-18494-4_2