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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Banach algebras with uncomplemented radical


Authors: Gregory F. Bachelis and Sadahiro Saeki
Journal: Proc. Amer. Math. Soc. 100 (1987), 271-274
MSC: Primary 46J20; Secondary 43A45
MathSciNet review: 884465
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Abstract: A condition is given on the invertible elements of a commutative Banach algebra $ \mathbf{B}$ which implies that the radical of $ \mathbf{B}$ is not complemented by any closed subalgebra. This condition is then applied to show that certain quotient algebras of group algebras have an uncomplemented radical.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0884465-0
PII: S 0002-9939(1987)0884465-0
Article copyright: © Copyright 1987 American Mathematical Society