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Banach function algebras with dense invertible group
Author(s):
H.
G.
Dales;
J.
F.
Feinstein
Journal:
Proc. Amer. Math. Soc.
136
(2008),
1295-1304.
MSC (2000):
Primary 46J10
Posted:
December 21, 2007
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Abstract:
In 2003 Dawson and Feinstein asked whether or not a Banach function algebra with dense invertible group can have a proper Shilov boundary. We give an example of a uniform algebra showing that this can happen, and investigate the properties of such algebras. We make some remarks on the topological stable rank of commutative, unital Banach algebras. In particular, we prove that  whenever  is approximately regular.
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Additional Information:
H.
G.
Dales
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
Email:
garth@maths.leeds.ac.uk
J.
F.
Feinstein
Affiliation:
School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
Email:
Joel.Feinstein@nottingham.ac.uk
DOI:
10.1090/S0002-9939-07-09044-2
PII:
S 0002-9939(07)09044-2
Received by editor(s):
December 1, 2005
Received by editor(s) in revised form:
October 23, 2006 and December 20, 2006
Posted:
December 21, 2007
Communicated by:
N. Tomczak-Jaegermann
Copyright of article:
Copyright
2007,
American Mathematical Society
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