Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-30T21:38:52.291Z Has data issue: false hasContentIssue false
  • English
  • Français

DISCONTINUOUS HOMOMORPHISMS FROM NON-COMMUTATIVE BANACH ALGEBRAS

Published online by Cambridge University Press:  01 July 1997

H. G. DALES  and
V. RUNDE
H. G. DALES
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT
V. RUNDE
Affiliation:
Fachbereich 9 Mathematik, Universität des Saarlandes, Postfach 151150, 66041 Saarbrücken, Germany
Get access

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 [mid ]A/P[mid ]=2ℵ0 [4, 8]. (It is an open question whether or not every infinite-dimensional, commutative Banach algebra A satisfies this latter condition.)

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 4 , July 1997 , pp. 475 - 479
Copyright
© The London Mathematical Society 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)