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Prime ideals in algebras of continuous functions

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Prime ideals in algebras of continuous functions. / Dales, H.G.; Loy, Richard J.

In: Proceedings of the American Mathematical Society, Vol. 98, No. 3, 1986, p. 426-430.

Research output: Contribution to journalJournal articlepeer-review

Harvard

Dales, HG & Loy, RJ 1986, 'Prime ideals in algebras of continuous functions', Proceedings of the American Mathematical Society, vol. 98, no. 3, pp. 426-430. https://doi.org/10.1090/S0002-9939-1986-0857934-6

APA

Dales, H. G., & Loy, R. J. (1986). Prime ideals in algebras of continuous functions. Proceedings of the American Mathematical Society, 98(3), 426-430. https://doi.org/10.1090/S0002-9939-1986-0857934-6

Vancouver

Dales HG, Loy RJ. Prime ideals in algebras of continuous functions. Proceedings of the American Mathematical Society. 1986;98(3):426-430. https://doi.org/10.1090/S0002-9939-1986-0857934-6

Author

Dales, H.G. ; Loy, Richard J. / Prime ideals in algebras of continuous functions. In: Proceedings of the American Mathematical Society. 1986 ; Vol. 98, No. 3. pp. 426-430.

Bibtex

@article{81893ef484a54783b847e5f5a48a1771,
title = "Prime ideals in algebras of continuous functions",
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.",
author = "H.G. Dales and Loy, {Richard J.}",
year = "1986",
doi = "10.1090/S0002-9939-1986-0857934-6",
language = "English",
volume = "98",
pages = "426--430",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "3",

}

RIS

TY - JOUR

T1 - Prime ideals in algebras of continuous functions

AU - Dales, H.G.

AU - Loy, Richard J.

PY - 1986

Y1 - 1986

N2 - 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.

AB - 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.

U2 - 10.1090/S0002-9939-1986-0857934-6

DO - 10.1090/S0002-9939-1986-0857934-6

M3 - Journal article

VL - 98

SP - 426

EP - 430

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 3

ER -