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 $f\in A$ we denote by $\hat f$ the Gelfand transform of $f$ defined on $\hat A$, the set of maximal ideals of $A$. Let $(f_1,\dots,f_n)\in A^n$ be such that $\sum_{i=1}^n\|f_i\|^2 \leq 1$. We study here the existence of solutions $(g_1,\dots,g_n)\in A^n$ to the Bezout equation $f_1g_1+\cdots+f_ng_n=e$, whose norm is controlled by a function of $n$ and $\delta=\inf_{\chi\in\hat A}(|\hat f_1(\chi)|^2+\cdots+|\hat f_n(\chi)|^2)^{1/2}$. 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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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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Section

Articles