Lancaster EPrints

Uniqueness of the norm topology for Banach algebras with finite-dimensional radical

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

Full text not available from this repository.

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
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

Actions (login required)

View Item