Estimations des solutions de l'équation de Bezout dans les algèbres de Beurling analytiques
DOI:
https://doi.org/10.7146/math.scand.a-14959Abstract
Let A be a unitary commutative Banach algebra with unit e. For f∈A 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=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∈ˆA(|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
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