TY - JOUR

T1 - Banach function algebras with dense invertible group

AU - Dales, H.G.

AU - Feinstein, J. F.

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

U2 - 10.1090/S0002-9939-07-09044-2

DO - 10.1090/S0002-9939-07-09044-2

M3 - Journal article

VL - 136

SP - 1295

EP - 1304

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 1088-6826

IS - 4

ER -