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Journal of the London Mathematical Society 2002 65(3):705-719; doi:10.1112/S0024610701003088
© 2002 by London Mathematical Society
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© The London Mathematical Society

Majorations Uniformes de Normes D'Inverses Dans Les Algèbres de Beurling

O. El-Fallah and A. Ezzaaraoui

Departement de Mathématiques et Informatique, Faculté des Sciences, Université Mohammed V Avenue Ibn Battouta, BP 1014, Rabat, Morocco, elfallah{at}fsr.ac.ma
Departement de Mathématiques et Informatique, Faculté des Sciences, Université Mohammed V Avenue Ibn Battouta, BP 1014, Rabat, Morocco

Received 18 May 2000. Revision received 1 May 2001.

The Beurling algebras l1(D,{omega})(D=N,Z) that are semi-simple, with compact Gelfand transform, are considered. The paper gives a necessary and sufficient condition (on {omega}) such that l1(D,{omega}) possesses a uniform quantitative version of Wiener's theorem in the sense that there exists a function {phi}:]0,+{infty}[->]0,+{infty} such that, for every invertible element x in the unit ball of l1(D,{omega}), we have

||x–1||≤{phi}(r(x–1)) r(x–1) is the spectral radius of x–1.


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