Estimations des solutions de l'équation de Bezout dans les algèbres de Beurling analytiques

Authors

  • O. El-Fallah
  • M. Zarrabi

DOI:

https://doi.org/10.7146/math.scand.a-14959

Abstract

Let A be a unitary commutative Banach algebra with unit e. For fA we denote by ˆf the Gelfand transform of f defined on ˆA, the set of maximal ideals of A. Let (f1,,fn)An be such that ni=1fi21. We study here the existence of solutions (g1,,gn)An to the Bezout equation f1g1++fngn=e, whose norm is controlled by a function of n and δ=infχˆA(|ˆf1(χ)|2++|ˆfn(χ)|2)1/2. We treat this problem for the analytic Beurling algebras and their quotient by closed ideals. The general Banach algebras with compact Gelfand transform are also considered.

Downloads

Published

2005-06-01

How to Cite

El-Fallah, O., & Zarrabi, M. (2005). Estimations des solutions de l’équation de Bezout dans les algèbres de Beurling analytiques. MATHEMATICA SCANDINAVICA, 96(2), 307–319. https://doi.org/10.7146/math.scand.a-14959

Issue

Section

Articles