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On the Arens semi-regularity of weighted group algebras

Published online by Cambridge University Press:  18 May 2009

Ziya Argün  and
K. Rowlands
Ziya Argün
Affiliation:
Department of Mathematics, Faculty of Education, Gazi University, Teknik-Okullar, Ankara, Turkey
K. Rowlands
Affiliation:
Department of Mathematics, University of Wales, Aberystwyth, Dyfed, UK
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Abstract

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In this paper we prove that the weighted group algebra L1 (G, w) is semi-regular if and only if G is either abelian or discrete.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 36 , Issue 3 , September 1994 , pp. 269 - 275
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

References

REFERENCES

1.Bonsall, F. F. and Duncan, J., Complete normed algebras (Springer-Verlag, 1973).CrossRefGoogle Scholar
2.Duncan, J. and Hossenium, S. R. R., The second dual of a Banach algebra, Proc. Roy. Soc. Edinburgh, Sect A 84 (1979), 309–325.CrossRefGoogle Scholar
3.Gaundry, G. I., Multipliers of weighted Lebesgue and measure spaces, Proc. London Math. Soc. (3) 19 (1969), 327–340.CrossRefGoogle Scholar
4.Granirer, E. E., The radical of (L∞(G))*, Proc. Amer. Math. Soc., 41 (1973), 321–4.Google Scholar
5.Grosser, M., Arens semi-regular Banach algebras, Monatsh. Math. 98 (1984), 41–52.CrossRefGoogle Scholar
6.Grosser, M., Arens semi-regularity of the algebra of compact operators, Illinois J. Math. 31 (1987), 554–573.CrossRefGoogle Scholar
7.Hewitt, E. and Ross, K. A., Abstract harmonic analysis I (Springer-Verlag, 1963).Google Scholar
8.Losert, V. and Rindler, H., Asymptotically central functions and invariant extensions of Dirac measures, in Probability measures on groups, VII (Oberwolfach, 1983), Lecture notes in Mathematics N, 1064 (Springer-Verlag, 1984), 368–378.CrossRefGoogle Scholar
9.Reiter, H., Classical harmonic analysis and locally compact groups (Oxford University Press, 1968).Google Scholar
10.Tomiuk, B. J., Multipliers on Banach algebras, Studia Math. 54 (1976), 267–283.CrossRefGoogle Scholar
11.Ülger, A., Arens regularity sometimes implies the R. N. P., Pacific J. Math. 143 (1990), 377–399.CrossRefGoogle Scholar
12.Wong, Pak-Ken, Arens product and the algebra of double multipliers, Proc. Amer. Math. Soc. 94 (1985), 441–444.CrossRefGoogle Scholar
13.Young, N. J., The irregularity of multiplication in group algebras, Quart. J. Math. 24 (1973), 59–62.CrossRefGoogle Scholar
14.Young, N. J., Periodicity of functionals and representations of normed algebras on reflexive spaces, Proc. Edinburgh Math. Soc. 20 (1976), 99–120.CrossRefGoogle Scholar