Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The kernels of radical homomorphisms and intersections of prime ideals


Author: Hung Le Pham
Journal: Trans. Amer. Math. Soc. 360 (2008), 1057-1088
MSC (2000): Primary 46H40, 46J10; Secondary 46J05, 13C05, 43A20
Published electronically: July 23, 2007
MathSciNet review: 2346483
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We establish a necessary condition for a commutative Banach algebra $ A$ so that there exists a homomorphism $ \theta$ from $ A$ into another Banach algebra such that the prime radical of the continuity ideal of $ \theta$ is not a finite intersection of prime ideals in $ A$. We prove that the prime radical of the continuity ideal of an epimorphism from $ A$ onto another Banach algebra (or of a derivation from $ A$ into a Banach $ A$-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.


References [Enhancements On Off] (What's this?)


Similar Articles

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

Retrieve articles in all journals with MSC (2000): 46H40, 46J10, 46J05, 13C05, 43A20


Additional Information

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: http://dx.doi.org/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
Published electronically: July 23, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.