Transactions of the American Mathematical Society

Author(s): Hung Le Pham
Journal: Trans. Amer. Math. Soc. 360 (2008), 1057-1088.
MSC (2000): Primary 46H40, 46J10; Secondary 46J05, 13C05, 43A20
Posted: July 23, 2007
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Abstract: We establish a necessary condition for a commutative Banach algebra

so that there exists a homomorphism $\theta$ from

into another Banach algebra such that the prime radical of the continuity ideal of $\theta$ is not a finite intersection of prime ideals in

. We prove that the prime radical of the continuity ideal of an epimorphism from

onto another Banach algebra (or of a derivation from

into a Banach

-bimodule) is always a finite intersection of prime ideals. Under an additional cardinality condition (and assuming the Continuum Hypothesis), this necessary condition is proved to be sufficient. En route, we give a general result on norming commutative semiprime algebras; extending the class of algebras known to be normable. We characterize those locally compact metrizable spaces $\Omega$ for which there exists a homomorphism from $\mathcal C_0(\Omega)$ into a radical Banach algebra whose kernel is not a finite intersection of prime ideals.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 46H40, 46J10, 46J05, 13C05, 43A20

Hung Le Pham
Affiliation: Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, England
Address at time of publication: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2E1
Email: hung@maths.leeds.ac.uk, hlpham@math.ualberta.ca

DOI: 10.1090/S0002-9947-07-04325-5
PII: S 0002-9947(07)04325-5
Keywords: Banach algebra, algebra of continuous functions, automatic continuity, commutative algebra, prime ideal, locally compact space, locally compact group
Received by editor(s): June 1, 2005
Received by editor(s) in revised form: April 7, 2006
Posted: July 23, 2007
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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