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Automatic continuity for Banach algebras with finite-dimensional radical

Part of: Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  09 April 2009

Hung Le Pham
Hung Le Pham
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, UK, e-mail: hung@maths.leeds.ac.uk
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Abstract

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The paper [3] proved a necessary algebraic condition for a Banach algebra A with finite-dimensional radical R to have a unique complete (algebra) norm, and conjectured that this condition is also sufficient. We extend the above theorem. The conjecture is confirmed in the case where A is separable and A/R is commutative, but is shown to fail in general. Similar questions for derivations are discussed.

Keywords

Banach algebrauniqueness of normautomatic continuityderivationfinite-dimensional.

MSC classification

Secondary: 46H40: Automatic continuity
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 81 , Issue 2 , October 2006 , pp. 279 - 296
Copyright
Copyright © Australian Mathematical Society 2006

References

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