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Topologically Irreducible Representations and Radicals in Banach Algebras
Author(s) -
Dixon PG
Publication year - 1997
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611597000075
Subject(s) - jacobson radical , mathematics , radical , transitive relation , pure mathematics , prime (order theory) , irreducible representation , algebra over a field , combinatorics , chemistry , ring (chemistry) , organic chemistry
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.