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

Official URL: https://doi.org/10.1090/S0002-9939-07-09044-2

## 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

Last Modified:

09 Feb 2021 04:18