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Topologically irreducible representations and radicals in Banach algebras

Published online by Cambridge University Press:  01 January 1997

PG Dixon
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Abstract

It is shown that the topologically irreducible representations of a normed algebra define a certain topological radical in the same way that the strictly irreducible representations define the Jacobson radical and that this radical can be strictly smaller than the Jacobson radical. An abstract theory of ‘topological radicals’ in topological algebras is developed and used to relate this radical to the Baer radical (prime radical). The relations with topologically transitive representations and standard representations in the sense of Meyer are also explored.

1991 Mathematics Subject Classification: 46H15, 46H25, 16Nxx.

Keywords

topologically irreducible representationstandard representationBaer radicalprime radicalsemiprime algebraJacobson radicalBanach algebrainvariant subspace problem
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 74 , Issue 1 , January 1997 , pp. 174 - 200
Copyright
London Mathematical Society 1997

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