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Representations of bornological algebras

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Abstract

Bounded representations of bornological algebras are considered. The left and right bornological radicals in bornological algebras are introduced. It is shown that the left (right) bornological radical of a bornological algebra A is equal to the intersection of all bornologically closed maximal regular left (respectively, right) ideals of A, and both these radicals of A and the Jacobson radical of A coincide if A is an advertive and simplicial bornological algebra (in particular, a bornological Q-algebra). Bibliography: 16 titles.

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Authors and Affiliations

  1. Institute of Pure Mathematics, University of Tartu, Estonia

    M. Abel

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  1. M. Abel
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 326, 2005, pp. 9–22.

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Abel, M. Representations of bornological algebras. J Math Sci 140, 346–353 (2007). https://doi.org/10.1007/s10958-007-0443-4

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  • DOI: https://doi.org/10.1007/s10958-007-0443-4

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