Estimations des solutions de l'equation de Bezout dans les algebres de Beurling analytiques
- Autores: O. El-Fallah
- Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 96, Nº 2, 2005, págs. 307-319
- Idioma: inglés
- DOI: 10.7146/math.scand.a-14959
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Resumen
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.
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