Estimations des solutions de l’équation de Bezout dans les algèbres de Beurling analytiques - El-Fallah, O.; Zarrabi, M. (MATHEMATICA SCANDINAVICA, 2005)
Let A be a unitary commutative Banach algebra with unit e. For fA we denote by f the Gelfand transform of f defined on A, the set of maximal ideals of A. Let (f_1,…,f_n)A^n be such that _i=1^n\|f_i\|^2 ≤ 1. We study here the existence of solutions (g_1,…,g_n)A^n to the Bezout equation f_1g_1+…+f_ng_n=e, whose norm is controlled by a function of n and δ=_χA(|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.