Topologically Irreducible Representations and Radicals in Banach Algebras |
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Authors: | Dixon PG |
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Institution: | Pure Mathematics Section, School of Mathematics and Statistics, University of Sheffield Sheffield S3 7RH, UK. Email: p.dixon{at}sheffield.ac.uk |
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Abstract: | It is shown that the topologically irreducible representationsof a normed algebra define a certain topological radical inthe same way that the strictly irreducible representations definethe Jacobson radical and that this radical can be strictly smallerthan the Jacobson radical. An abstract theory of topologicalradicals in topological algebras is developed and usedto relate this radical to the Baer radical (prime radical).The relations with topologically transitive representationsand standard representations in the sense of Meyer are alsoexplored. 1991 Mathematics Subject Classification: 46H15, 46H25,16Nxx. |
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Keywords: | topologically irreducible representation standard representation Baer radical prime radical semiprime algebra Jacobson radical Banach algebra invariant subspace problem |
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