Home > Research > Publications & Outputs > Banach function algebras with dense invertible ...

## Banach function algebras with dense invertible group

Research output: Contribution to journalJournal articlepeer-review

Published
Close
Journal publication date 2008 Proceedings of the American Mathematical Society 4 136 10 1295-1304 Published 21/12/07 English

### 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.