Resumen de Estimations des solutions de l'equation de Bezout dans les algebres de Beurling analytiques
Let A be a unitary commutative Banach algebra with unit e. For f∈A we denote by f^ the Gelfand transform of f defined on A^, the set of maximal ideals of A. Let (f1,…,fn)∈An be such that ∑ni=1∥fi∥2≤1. 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=infχ∈A^(|f^1(χ)|2+⋯+|f^n(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.
