# Banach function algebras with dense invertible group

Dales, H.G. and Feinstein, J. F. (2008) Banach function algebras with dense invertible group. Proceedings of the American Mathematical Society, 136 (4). pp. 1295-1304. ISSN 1088-6826

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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.

Item Type:
Journal Article
Journal or Publication Title:
Proceedings of the American Mathematical Society
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600
Subjects:
Departments:
ID Code:
67580
Deposited By:
Deposited On:
19 Nov 2013 09:04
Refereed?:
Yes
Published?:
Published