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:
Journal Article
Journal or Publication Title:
Bulletin of the London Mathematical Society
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600
Subjects:
ID Code:
67609
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Deposited On:
20 Nov 2013 11:24
Refereed?:
Yes
Published?:
Published
Last Modified:
01 Jan 2020 08:42