Prime ideals in algebras of continuous functions

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

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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
Journal or Publication Title: Proceedings of the American Mathematical Society
Uncontrolled Keywords: /dk/atira/pure/subjectarea/asjc/2600
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: 01 Jan 2020 08:43

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