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Minimal ideals in group algebras and their biduals

Published online by Cambridge University Press:  24 October 2008

J. W. Baker  and
M. Filali
J. W. Baker
Affiliation:
School of Mathematics & Statistics, University of Sheffield, Sheffield S3 7RH
M. Filali
Affiliation:
Department of Mathematics, University of Oulu, Oulu 90570, Finland
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Abstract

Let G be a locally compact group and F a left introverted subalgebra of C(G). For each of the algebras L1(G), M(G), F* and L∞(G)* we determine the finite-dimensional minimal left ideals of the algebra (if any); in some cases we also determine the finite-dimensional minimal two-sided ideals, and in certain cases show that all minimal ideals of the algebra are finite-dimensional.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 120 , Issue 3 , October 1996 , pp. 475 - 488
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

REFERENCES

[1]Berlund, J. F., Junghenn, H. D. and Milnes, P.. Analysis on semigroups: function spaces, compactifications, representations (Wiley, 1989).Google Scholar
[2]Bonsall, F. F. and Duncan, J.. Complete normed algebras (Springer-Verlag, 1973).CrossRefGoogle Scholar
[3]Filali, M.. The uniform compactification of a locally compact abelian group. Math. Proc. Cambridge Philos. Soc. 108 (1990), 527–538.CrossRefGoogle Scholar
[4]Filali, M.. The ideal structure of some Banach algebras. Math. Proc. Cambridge Philos. Soc. 111 (1992), 567–576.CrossRefGoogle Scholar
[5]Filali, M.. Linear equations in B(ℤ). Math. Proc. Roy. Soc. Edinburgh, Series A 123 (1993), 1001–1009.CrossRefGoogle Scholar
[6]Hewitt, E. and Ross, K. A.. Abstract harmonic analysis, vol. 1 (Springer-Verlag, 1963).Google Scholar
[7]Hewitt, E. and Ross, K. A.. Abstract harmonic analysis, vol. 2 (Springer-Verlag, 1970).Google Scholar
[8]Lashkarizadeh-Bami, M.. Representations of foundation semigroups and their algebras. Canadian J. Math. 37 (1985), 29–47.CrossRefGoogle Scholar
[9]Loomis, L. H.. An introduction to abstract harmonic analysis (Van Nostrand, 1953).Google Scholar
[10]Paterson, A. L. T.. Amenability (American Mathematical Society, 1988).CrossRefGoogle Scholar
[11]Pym, J. S.. Compact semigroups with one-sided continuity; in The analytical and topological theory of semigroups (ed.Hoffman, K. H. et al. , de Gruyter, 1990), 197–217.CrossRefGoogle Scholar
[12]Rickart, C. E.. General theory of Banach algebras (Van Nostrand, 1960).Google Scholar