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Banach function algebras with dense invertible group

Authors: H. G. Dales and J. F. Feinstein
Journal: Proc. Amer. Math. Soc. 136 (2008), 1295-1304
MSC (2000): Primary 46J10
Published electronically: December 21, 2007
MathSciNet review: 2367103
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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 $ \mathrm{tsr}(A) \geq \mathrm{tsr}(C(\Phi_A))$ whenever $ A$ 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

J. F. Feinstein
Affiliation: School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom

Received by editor(s): December 1, 2005
Received by editor(s) in revised form: October 23, 2006, and December 20, 2006
Published electronically: December 21, 2007
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2007 American Mathematical Society

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