Proceedings of the Edinburgh Mathematical Society (Series 2)
- Proceedings of the Edinburgh Mathematical Society (Series 2) / Volume 36 / Issue 03 / October 1993, pp 421-425
- Copyright © Edinburgh Mathematical Society 1993
- DOI: http://dx.doi.org/10.1017/S0013091500018514 (About DOI), Published online: 20 January 2009
Research Article
On the closure of the prime radical of a Banach algebra
D. W. B. Somerseta1 and G. A. Willisa2 p1
a1 ‘Thakit Eaves’, Highclere, Near Newbury, Berkshire, RG15 9QU, United Kingdom
a2 Mathematics Research Section, Australian National University, Canberra, A.C.T., 2600, Australia
Abstract
The relationship between the prime ideals and the primal ideals of a Banach algebra is investigated. It is shown that the closure of the prime radical of a Banach algebra may be properly contained in the intersection of the closed primal ideals of the algebra.
(Received November 04 1991)
Correspondence:
p1 Department of Mathematics, The University of Newcastle, New South Wales, 2308, Australia
- 1. Archbold, R. J., Topologies for primal ideals, J. London Math. Soc. (2) 36 (1987), 524–542. [OpenURL Query Data] [CrossRef] [Google Scholar]
- 2. Archbold, R. J. and Somerset, D. W. B., Quasi-standard C*-algebras, Math. Proc. Cambridge Philos. Soc. 107 (1990), 349–360. [OpenURL Query Data] [CrossRef] [Google Scholar]
- 3. Dixon, P. G., Semiprime Banach algebras, J. London Math Soc. (2) 6 (1973), 676–678. [OpenURL Query Data] [CrossRef] [Google Scholar]
- 4. Grabiner, S., Nilpotents in Banach algebras, J. London Math. Soc. (2) 14 (1976), 7–12. [OpenURL Query Data] [CrossRef] [Google Scholar]
- 5. Somerset, D. W. B., Minimal primal ideals in Banach algebras, in preparation.
