Dales, H.G. and Loy, Richard J. (1986) *Prime ideals in algebras of continuous functions.* Proceedings of the American Mathematical Society, 98 (3). pp. 426-430. ISSN 0002-9939

## Abstract

Let $ {X_0}$ be a compact Hausdorff space, and let $ {\mathbf{C}}({X_0})$ be the Banach algebra of all continuous complex-valued functions on $ {X_0}$. It is known that, assuming the continuum hypothesis, any nonmaximal, prime ideal $ {\mathbf{P}}$ such that $ \vert{\mathbf{C}}({X_0})/{\mathbf{P}}\vert = {2^{{\aleph _0}}}$ is the kernel of a discontinuous homomorphism from $ {\mathbf{C}}({X_0})$ into some Banach algebra. Here we consider the converse question of which ideals can be the kernels of such a homomorphism. Partial results are obtained in the case where $ {X_0}$ is metrizable.

Item Type: | Journal Article |
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Journal or Publication Title: | Proceedings of the American Mathematical Society |

Subjects: | |

Departments: | Faculty of Science and Technology > Mathematics and Statistics |

ID Code: | 67636 |

Deposited By: | ep_importer_pure |

Deposited On: | 21 Nov 2013 11:49 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 11 Apr 2018 01:14 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/67636 |

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