|
Non-closed sums of closed ideals in Banach algebras
Author(s):
P.
G.
Dixon
Journal:
Proc. Amer. Math. Soc.
128
(2000),
3647-3654.
MSC (2000):
Primary 46H10;
Secondary 46J20, 46J15
Posted:
June 21, 2000
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
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:
- 1.
- F. Combes, Sur les faces d'une C*-algèbre Bull. Sci. Math., 93 (1969), 37-62. MR 42:856
- 2.
- A. M. Davie, Quotient algebras of uniform algebras, J. London Math. Soc. (2), 7 (1973), 31-40. MR 48:2779
- 3.
- J. Dixmier, Les C*-algèbres et leurs représentations, Gauthier-Villars, Paris, 1964. MR 30:1404
- 4.
- P. G. Dixon, Topologically irreducible representations and radicals in Banach algebras, Proc. London Math. Soc. (3), 74 (1997), 174-200. MR 30:46066
- 5.
- Robert S. Doran and Josef Wichmann, Approximate Identities and Factorization in Banach Modules, Springer, Lecture Notes in Math., 768, Berlin, 1979. MR 83e:46044
- 6.
- E. Kirchberg, On restricted perturbations in inverse images and a description of normalizer algebras in C*-algebras, J. Functional Analysis, 129 (1995), 1-34. MR 95m:46094a
- 7.
- W. Rudin, Spaces of type
 , Ann. Inst. Fourier, Grenoble, 25 (1975), 99-125. MR 57:13692; errata MR 57:7134 - 8.
- D. A. Stegenga, Ideals in the disk algebra, J. Functional Analysis, 25 (1977), 335-337. MR 58:2307
- 9.
- Simon Wassermann, Exact C*-algebras and related topics, Research Institute of Mathematics, Global Analysis Research Center, Seoul National University, Lecture Note Series, 19, 1994. MR 95b:46081
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
46H10,
46J20, 46J15
Retrieve articles in all Journals with MSC
(2000):
46H10,
46J20, 46J15
Additional Information:
P.
G.
Dixon
Affiliation:
Department of Pure Mathematics, University of Sheffield, Sheffield, S3 7RH, England
Email:
P.Dixon@sheffield.ac.uk
DOI:
10.1090/S0002-9939-00-05700-2
PII:
S 0002-9939(00)05700-2
Received by editor(s):
March 1, 1999
Posted:
June 21, 2000
Communicated by:
David R. Larson
Copyright of article:
Copyright
2000,
American Mathematical Society
|
Comments: webmaster@ams.org