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

 

Non-closed sums of closed ideals in Banach algebras


Author: P. G. Dixon
Journal: Proc. Amer. Math. Soc. 128 (2000), 3647-3654
MSC (2000): Primary 46H10; Secondary 46J20, 46J15
Published electronically: June 21, 2000
MathSciNet review: 1778282
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Abstract:

A major difficulty in Banach algebra theory is that sums of closed ideals need not be closed. We survey the known results and present examples showing that they are in most directions the best possible. We also give a new sufficient condition for closure in the uniform algebra setting.


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Additional Information

P. G. Dixon
Affiliation: Department of Pure Mathematics, University of Sheffield, Sheffield, S3 7RH, England
Email: P.Dixon@sheffield.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05700-2
PII: S 0002-9939(00)05700-2
Received by editor(s): March 1, 1999
Published electronically: June 21, 2000
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society