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Non commutative convolution measure algebras with no proper L-ideals

Published online by Cambridge University Press:  17 April 2009

Sahl Fadul Albar
Sahl Fadul Albar
Affiliation:
Department of Mathematical SciencesUmm Al Qura UniversityMakkahSaudi Arabia
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Abstract

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We study non-commutative convolution measure algebras satisfying the condition in the title and having an involution with a non-degenerate finite dimensional *-representation. We show first that the group algebra L1(G) of a locally compact group G satisfies these conditions. Then we show that to a given algebra A with the above conditions there corresponds a locally compact group G such that A is a * and L-subalgebra of M(G) and such that the enveloping C*-algebra of A is *isomorphic to C*(G). Finally we show for certain groups that L1(G) is the only example of such algebras, thus giving a characterisation of L1(G).

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 40 , Issue 1 , August 1989 , pp. 13 - 23
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Dixmier, J., C*-algebras (North Holland Publishing Co., 1977).Google Scholar
[2]Eymard, P., ‘L'Algebre de Fourier d'un groupe localement Compact’, Bull. Soc. Math. Franc 92 (1964), 181–236.CrossRefGoogle Scholar
[3]Hewitt, E. and Ross, K.A., Abstract Harmonic Analysis I (Springer Verlag, 1963).Google Scholar
[4]Mosak, R.D., ‘The L 1 and C*-algebra of groups and their representations’, Trans. Amer. Math. Soc. 163 (1972), 277–310.Google Scholar
[5]Taylor, J.L., ‘Non Commutative Convolution Measure algebras’, Pacific I. Math. 31 (1969), 809–826.CrossRefGoogle Scholar
[6]Taylor, J.L., ‘Measure algebras’, Trans. Amer. Math. Soc. (1973).Google Scholar
[7]Taylor, J.L., ‘Convolution Measure algebras with group maximal ideal spaces’, Trans. Amer. Math. Soc. 128 (1967), 257–263.Google Scholar