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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The relative completion of an $ A$-Segal algebra is closed


Author: James T. Burnham
Journal: Proc. Amer. Math. Soc. 49 (1975), 116-122
MSC: Primary 46H10; Secondary 43A20
DOI: https://doi.org/10.1090/S0002-9939-1975-0361786-3
MathSciNet review: 0361786
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Abstract: The main result is this theorem: If the Banach algebra $ A$ has bounded approximate right units and $ B$ is an $ A$-Segal algebra, then the relative completion of $ B$ with respect to $ A$ is an $ A$-Segal algebra. Furthermore, $ B$ is a closed ideal of its relative completion with respect to $ A$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0361786-3
Keywords: Banach algebras, Banach modules, closed ideals, approximate identities, Segal algebras
Article copyright: © Copyright 1975 American Mathematical Society