Mortini, Raymond, Rupp, Rudolf, Sasane, Amol and Wick, Brett D.
(2010)
*Topological stable rank of H ∞(Ω) for circular domains Ω.*
Analysis Mathematica, 36
(4).
pp. 287-297.
ISSN 0133-3852

## Abstract

Let Ω be a circular domain, that is, an open disk with finitely many closed disjoint disks removed. Denote by H ∞(Ω) the Banach algebra of all bounded holomorphic functions on Ω, with pointwise operations and the supremum norm. We show that the topological stable rank of H ∞(Ω) is equal to 2. The proof is based on Suárez’s theorem that the topological stable rank of H ∞($ \mathbb{D} $D) is equal to 2, where $ \mathbb{D} $D is the unit disk. We also show that for circular domains symmetric to the real axis, the Bass and topological stable ranks of the real-symmetric algebra H ℝ∞ (Ω) are 2.

Item Type: | Article |
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Official URL: | http://www.springer.com/mathematics/analysis/journ... |

Additional Information: | © 2010 Springer |

Library of Congress subject classification: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Rights: | http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx |

Date Deposited: | 28 Jul 2011 09:13 |

URL: | http://eprints.lse.ac.uk/37642/ |

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