Non-closed sums of closed ideals in Banach algebras
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- by P. G. Dixon PDF
- Proc. Amer. Math. Soc. 128 (2000), 3647-3654 Request permission
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.References
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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
- Received by editor(s): March 1, 1999
- Published electronically: June 21, 2000
- Communicated by: David R. Larson
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 3647-3654
- MSC (2000): Primary 46H10; Secondary 46J20, 46J15
- DOI: https://doi.org/10.1090/S0002-9939-00-05700-2
- MathSciNet review: 1778282