Dales, H.G. and Loy, Richard J. (1997) *Uniqueness of the norm topology for Banach algebras with finite-dimensional radical.* Proceedings of the London Mathematical Society, 74 (3). pp. 633-661. ISSN 0024-6115

## Abstract

Semisimple Banach algebras are well-known to have a unique (complete) algebra norm topology, but such uniqueness may fail if the radical is even one-dimensional. We obtain a necessary condition for uniqueness of norm when the algebra has finite-dimensional radical. In the case where the Banach algebra is separable, the condition is shown to be also sufficient for a large class of algebras, and in particular under various hypotheses of commutativity. Examples are given to show the limitations of the various sufficiency results, and these also give a good indication of where the difficulties lie in general. We conjecture that, at least in the separable case, our condition is both necessary and sufficient.

Item Type: | Article |
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Journal or Publication Title: | Proceedings of the London Mathematical Society |

Uncontrolled Keywords: | Banach algebras ; uniqueness of norm ; radical ; analytic space |

Subjects: | |

Departments: | Faculty of Science and Technology > Mathematics and Statistics |

ID Code: | 67610 |

Deposited By: | ep_importer_pure |

Deposited On: | 20 Nov 2013 11:28 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 20 Nov 2017 11:16 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/67610 |

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