Research output: Contribution to journal › Journal article

Published

<mark>Journal publication date</mark> | 1986 |
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<mark>Journal</mark> | Proceedings of the American Mathematical Society |

Issue number | 3 |

Volume | 98 |

Number of pages | 5 |

Pages (from-to) | 426-430 |

Publication status | Published |

Original language | English |

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.