Banach function algebras with dense invertible group

Dales, H.; Feinstein, J.

doi:10.1090/S0002-9939-07-09044-2

Banach function algebras with dense invertible group
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by H. G. Dales and J. F. Feinstein PDF

Proc. Amer. Math. Soc. 136 (2008), 1295-1304 Request permission

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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