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Discontinuous homomorphisms from non-commutative Banach algebras

Dales, H.G. and Runde, Volker (1997) Discontinuous homomorphisms from non-commutative Banach algebras. Bulletin of the London Mathematical Society, 29 (4). pp. 475-479. ISSN 0024-6093

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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.)

Item Type: Article
Journal or Publication Title: Bulletin of the London Mathematical Society
Subjects:
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 67609
Deposited By: ep_importer_pure
Deposited On: 20 Nov 2013 11:24
Refereed?: Yes
Published?: Published
Last Modified: 20 Nov 2017 11:16
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/67609

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