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Amenability and ideals in A(G)

Part of: Abstract harmonic analysis Commutative Banach algebras and commutative topological algebras

Published online by Cambridge University Press:  09 April 2009

Brian Forrest
Brian Forrest
Affiliation:
Department of Pure MathematicsUniversity of WaterlooWaterloo Ontario, Canada
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Abstract

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Closed ideals in A(G) with bounded approximate identities are characterized for amenable [SIN]-groups and arbitrary discrete groups. This extends a result of Liu, van Rooij and Wang for abelian groups.

Keywords

Fourier algebraidealbounded approximate identityamenable.

MSC classification

Secondary: 43A07: Means on groups, semigroups, etc.; amenable groups 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc. 46J10: Banach algebras of continuous functions, function algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 53 , Issue 2 , October 1992 , pp. 143 - 155
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Cohen, P., ‘On homomorphisms of group algebras’, Amer. J. Math. 82 (1960), 213–226.CrossRefGoogle Scholar
[2]Cowling, M. and Rodway, P., ‘Restrictions of certain function spaces to closed subgroups of locally compact groups’, Pacific J. Math. 80 (1979), 91–104.CrossRefGoogle Scholar
[3]Eymard, P., ‘L'algèbre de Fourier d'un groupe localement compact’, Bull. Soc. Math. France 92 (1964), 181–236.CrossRefGoogle Scholar
[4]Eymard, P., Moyennes Invariantes et Représentations Unitaires (Lecture Notes in Math. vol. 300, Springer-Verlag, New York 1972).CrossRefGoogle Scholar
[5]Forrest, B., ‘Amenability and bounded approximate identities in ideals of A(G)’, Illinois J. Math. 34 (1990), 1–25.CrossRefGoogle Scholar
[6]Gaal, S., Linear Analysis and Representations Theory (Springer-Verlag, New York, 1973).CrossRefGoogle Scholar
[7]Gilbert, J., ‘On projections of L∞(G) onto translation-invariant subspaces’, Proc. London Math. Soc. 19 (1969), 69–88.CrossRefGoogle Scholar
[8]Herz, C., ‘Harmonic synthesis for subgroups’, Ann. Inst. Fourier (Grenoble) 23 (1973), 91–123.CrossRefGoogle Scholar
[9]Hewitt, E. and Ross, K. A., Abstract Harmonic Analysis vol. II (Springer-Verlag, New York, 1970).Google Scholar
[10]Host, B., ‘Le théorème des idempotents dans B(G)’, Bull. Soc. Math. France 114 (1986), 215–223.CrossRefGoogle Scholar
[11]Lau, A. T., ‘The second conjugate algebra of the Fourier algebra of a locally compact group’, Trans. Amer. Math. Soc. 267 (1981), 53–63.CrossRefGoogle Scholar
[12]Leptin, H., ‘Sur l'algèbre de Fourier d'un groupe localement compact’, C. R. Acad. Sci. Paris Sér. A 266 (1968), 1180–1182.Google Scholar
[13]Liu, T. S., Van Rooij, A. and Wang, J., ‘Projections and approximate identities for ideals in group algebras’, Trans. Amer. Math. Soc. 175 (1973), 469–482.CrossRefGoogle Scholar
[14]Mosak, R. D., ‘Central functions in group algebras’, Proc. Amer. Math. Soc. 29 (1971), 613–616.CrossRefGoogle Scholar
[15]Palmer, T. W., ‘Classes of nonabelian, noncompact, locally compact groups’, Rocky Mountain J. Math. 8 (1978), 683–739.CrossRefGoogle Scholar
[16]Reiter, H., Classical Harmonic Analysis and Locally Compact Groups (Oxford University Press, Oxford, 1968).Google Scholar
[17]Schreiber, B. M., ‘On the coset ring and strong Ditkin sets’, Pacific J. Math. 32 (1970), 805–812.CrossRefGoogle Scholar