Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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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 -