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

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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:
Journal Article
Journal or Publication Title:
Proceedings of the London Mathematical Society
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600
Subjects:
ID Code:
67610
Deposited By:
Deposited On:
20 Nov 2013 11:28
Refereed?:
Yes
Published?:
Published
Last Modified:
01 Jan 2020 08:42