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The strong radical and the left regular representation

Part of: Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  09 April 2009

B. J. Tomiuk  and
J. F. Price
B. J. Tomiuk
Affiliation:
Department of Mathematics, University of Ottawa, Ottawa, Ontario, K1N 9B4 Canada
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Abstract

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Let A be a semisimple modular annihilator Banach algebra and let LA be the left regular representation of A. We show how the strong radical of A is related to the strong radical of LA.

MSC classification

Secondary: 46H10: Ideals and subalgebras 46H15: Representations of topological algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 43 , Issue 1 , August 1987 , pp. 1 - 9
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Alexander, F. E., ‘On complemented and annihilator algebras’, Proc. Glascow Math. Assoc. 19 (1969), 38–45.Google Scholar
[2]Bachelis, G. F., ‘Homomorphisms of annihilator Banach algebras’, Pacific J. Math. 25 (1968), 229–247.CrossRefGoogle Scholar
[3]Barnes, B. A., ‘Modular annihilator algebras’, Canad. J. Math. 18 (1966), 566–578.CrossRefGoogle Scholar
[4]Leinert, M., ‘A contribution to Segal algebras’, Manuscripta Math. 10 (1975), 297–306.CrossRefGoogle Scholar
[5]Rickart, C. E., Banach algebras (Van Nostrand, 1960).Google Scholar
[6]Tomiuk, B. J., ‘Structure theory of complemented Banach algebras’, Canad. J. Math. 14 (1962), 651–659.CrossRefGoogle Scholar
[7]Tomiuk, B. J., ‘Isomorphisms of multiplier algebras’, Glascow Math. J., to appear.Google Scholar
[8]Tomiuk, B. J. and Yood, B., ‘Incomplete normed algebra norms on Banach algebras’, submitted.Google Scholar
[9]Yood, B., ‘Ideals in topological rings’, Canad. J. Math. 16 (1964), 28–45.CrossRefGoogle Scholar
[10]Yood, B., ‘Closed prime ideals in topological rings’, Proc. London Math. Soc. (3) 24 (1972), 307–323.CrossRefGoogle Scholar
[11]Yood, B., ‘On the strong radical of certain Banach algebras’, Proc. Edinburgh Math. Soc. 21 (1978), 81–85.CrossRefGoogle Scholar