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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the denseness of the invertible group in Banach algebras


Authors: T. W. Dawson and J. F. Feinstein
Journal: Proc. Amer. Math. Soc. 131 (2003), 2831-2839
MSC (2000): Primary 46J10, 46H05
Published electronically: April 7, 2003
MathSciNet review: 1974340
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Abstract: We examine the condition that a complex Banach algebra $A$ has dense invertible group. We show that, for commutative algebras, this property is preserved by integral extensions. We also investigate the connections with an old problem in the theory of uniform algebras.


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Additional Information

T. W. Dawson
Affiliation: Division of Pure Mathematics, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom
Email: pmxtwd@nottingham.ac.uk

J. F. Feinstein
Affiliation: Division of Pure Mathematics, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom
Email: Joel.Feinstein@nottingham.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07058-8
PII: S 0002-9939(03)07058-8
Received by editor(s): April 4, 2002
Published electronically: April 7, 2003
Additional Notes: The first author thanks the EPSRC for providing support for this research
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2003 American Mathematical Society