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The Range of Group Algebra Homomorphisms

Published online by Cambridge University Press:  20 November 2018

Andrew G. Kepert
Andrew G. Kepert*
Affiliation:
Department of Mathematics Central Coast Campus University of Newcastle Ourimbah, New South Wales 2258 Australia, e-mail: [email protected]
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Abstract

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A characterisation of the range of a homomorphism between two commutative group algebras is presented which implies, among other things, that this range is closed. The work relies mainly on the characterisation of such homomorphisms achieved by P. J. Cohen.

Keywords

Primary: 43A22secondary: 22B1046J99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 2 , 01 June 1997 , pp. 183 - 192
Copyright
Copyright © Canadian Mathematical Society 1997

References

1. Bourbaki, N., Éléments de Mathématique, Livre III, “Topologie Générale, 2me ed., Hermann, Paris, 1951.Google Scholar
2. Cohen, P. J., On a conjecture of Littlewood and idempotent measures, Amer. J. Math. 82 (1960), 191–212.Google Scholar
3. Cohen, P. J., On homomorphisms of group algebras, Amer. J. Math. 82 (1960), 213–226.Google Scholar
4. Forrest, B., Amenability and bounded approximate identites in ideals of A(G), Illinois J. Math. 34 (1990), 1–25.Google Scholar
5. Gilbert, John E., On projections of L1(G) onto translation-invariant subspaces, Proc. London Math. Soc. (3) 19 (1969), 69–88.Google Scholar
6. Greenleaf, Frederick P., Norm decreasing homomorphisms of group algebras, Pacific J. Math. 15 (1965), 1187–1219.Google Scholar
7. Hewitt, E. and Ross, K. A., Abstract Harmonic Analysis, 1, Springer-Verlag, Berlin, 1963; 2, Springer-Verlag, Berlin, 1970.Google Scholar
8. Host, B., Le Théorème des idempotents dans B(G), Bull. Soc. Math. France 114 (1986), 215–223.Google Scholar
9. Kalton, N. J. and Wood, G. V., Homomorphisms of group algebras with norm less than p2, Pac. J. Math. 62 (1976), 439–460.Google Scholar
10. Liu, T.-S., van Rooij, A. and Wang, J.-K., Projections and approximate identities for ideals in group algebras, Trans. Amer. Math. Soc. 175 (1973), 469–482.Google Scholar
11. Reiter, H., Classical Harmonic Analysis and Locally Compact Groups, Oxford Univ. Press, Oxford, 1968.Google Scholar
12. Rudin, W., Fourier Analysis on Groups, Interscience, New York, 1962.Google Scholar