Research output: Contribution to journal › Journal article

Published

<mark>Journal publication date</mark> | 07/1997 |
---|---|

<mark>Journal</mark> | Bulletin of the London Mathematical Society |

Issue number | 4 |

Volume | 29 |

Number of pages | 5 |

Pages (from-to) | 475-479 |

<mark>State</mark> | Published |

<mark>Original language</mark> | English |

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.)