Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-19T18:41:23.025Z Has data issue: false hasContentIssue false
  • English
  • Français

A Beurling algebra is semisimple: an elementary proof

Published online by Cambridge University Press:  17 April 2009

S. J. Bhatt  and
H. V. Dedania
S. J. Bhatt
Affiliation:
Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar - 388 120, Gujarat, India e-mail: sjb@spu.ernet.in, haresh@spu.ernet.in
H. V. Dedania
Affiliation:
Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar - 388 120, Gujarat, India e-mail: sjb@spu.ernet.in, haresh@spu.ernet.in
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 66 , Issue 1 , August 2002 , pp. 91 - 93
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Bhatt, S.J. and Dedania, H.V., ‘Banach algebras with unique uniform norm II’, Studia Math. 147 (2001), 211–235.Google Scholar
[2]Dzinotyiweyi, H.A.M., ‘Weighted function algebras on groups and semigroups’, Bull. Austral. Math. Soc. 33 (1986), 307–318.CrossRefGoogle Scholar
[3]Gelfand, I., Raikov, D. and Shilov, G., Commutative normed rings (Chelsea Publication Company, New York, 1964).Google Scholar
[4]Rudin, W., Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics 12 (Interscience Publishers, New York, London, 1962).Google Scholar
[5]White, M.C., ‘Characters on weighted amenable groups’, Bull. London Math. Soc. 23 (1991), 375–380.CrossRefGoogle Scholar