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**Discontinuous homomorphisms from non-commutative Banach algebras.** / Dales, H.G.; Runde, Volker.

Research output: Contribution to journal › Journal article

Dales, HG & Runde, V 1997, 'Discontinuous homomorphisms from non-commutative Banach algebras', *Bulletin of the London Mathematical Society*, vol. 29, no. 4, pp. 475-479. https://doi.org/10.1112/S0024609397002981

Dales, H. G., & Runde, V. (1997). Discontinuous homomorphisms from non-commutative Banach algebras. *Bulletin of the London Mathematical Society*, *29*(4), 475-479. https://doi.org/10.1112/S0024609397002981

Dales HG, Runde V. Discontinuous homomorphisms from non-commutative Banach algebras. Bulletin of the London Mathematical Society. 1997 Jul;29(4):475-479. https://doi.org/10.1112/S0024609397002981

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title = "Discontinuous homomorphisms from non-commutative Banach algebras",

abstract = "In the 1970s, a question of Kaplansky about discontinuous homomorphisms from certain commutative Banach algebras was resolved. Let A be the commutative C*-algebra C(Ω), where Ω is an infinite compact space. Then, if the continuum hypothesis (CH) be assumed, there is a discontinuous homomorphism from C(Ω) into a Banach algebra [2, 7]. In fact, let A be a commutative Banach algebra. Then (with (CH)) there is a discontinuous homomorphism from A into a Banach algebra whenever the character space ΦA of A is infinite [3, Theorem 3] and also whenever there is a non-maximal, prime ideal P in A such that ∣A/P∣=2ℵ0 [4, 8]. (It is an open question whether or not every infinite-dimensional, commutative Banach algebra A satisfies this latter condition.)",

author = "H.G. Dales and Volker Runde",

year = "1997",

month = "7",

doi = "10.1112/S0024609397002981",

language = "English",

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pages = "475--479",

journal = "Bulletin of the London Mathematical Society",

issn = "0024-6093",

publisher = "Oxford University Press",

number = "4",

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T1 - Discontinuous homomorphisms from non-commutative Banach algebras

AU - Dales, H.G.

AU - Runde, Volker

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N2 - In the 1970s, a question of Kaplansky about discontinuous homomorphisms from certain commutative Banach algebras was resolved. Let A be the commutative C*-algebra C(Ω), where Ω is an infinite compact space. Then, if the continuum hypothesis (CH) be assumed, there is a discontinuous homomorphism from C(Ω) into a Banach algebra [2, 7]. In fact, let A be a commutative Banach algebra. Then (with (CH)) there is a discontinuous homomorphism from A into a Banach algebra whenever the character space ΦA of A is infinite [3, Theorem 3] and also whenever there is a non-maximal, prime ideal P in A such that ∣A/P∣=2ℵ0 [4, 8]. (It is an open question whether or not every infinite-dimensional, commutative Banach algebra A satisfies this latter condition.)

AB - In the 1970s, a question of Kaplansky about discontinuous homomorphisms from certain commutative Banach algebras was resolved. Let A be the commutative C*-algebra C(Ω), where Ω is an infinite compact space. Then, if the continuum hypothesis (CH) be assumed, there is a discontinuous homomorphism from C(Ω) into a Banach algebra [2, 7]. In fact, let A be a commutative Banach algebra. Then (with (CH)) there is a discontinuous homomorphism from A into a Banach algebra whenever the character space ΦA of A is infinite [3, Theorem 3] and also whenever there is a non-maximal, prime ideal P in A such that ∣A/P∣=2ℵ0 [4, 8]. (It is an open question whether or not every infinite-dimensional, commutative Banach algebra A satisfies this latter condition.)

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DO - 10.1112/S0024609397002981

M3 - Journal article

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SP - 475

EP - 479

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

SN - 0024-6093

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ER -