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A Beurling algebra is semisimple: an elementary proof

  • S. J. Bhatt (a1) and H. V. Dedania (a1)

Abstract

The Beurling algebra L1(G,ω)on a locally compact Abelian group G with a measurable weight ω is shown to be semisimple. This gives an elementary proof of a result that is implicit in the work of M.C. White (1991), where the arguments are based on amenable (not necessarily Abelian) groups.

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References

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[1]Bhatt, S.J. and Dedania, H.V., ‘Banach algebras with unique uniform norm II’, Studia Math. 147 (2001), 211235.
[2]Dzinotyiweyi, H.A.M., ‘Weighted function algebras on groups and semigroups’, Bull. Austral. Math. Soc. 33 (1986), 307318.
[3]Gelfand, I., Raikov, D. and Shilov, G., Commutative normed rings (Chelsea Publication Company, New York, 1964).
[4]Rudin, W., Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics 12 (Interscience Publishers, New York, London, 1962).
[5]White, M.C., ‘Characters on weighted amenable groups’, Bull. London Math. Soc. 23 (1991), 375380.
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A Beurling algebra is semisimple: an elementary proof

  • S. J. Bhatt (a1) and H. V. Dedania (a1)

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