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| HAL: hal-00288491, version 1 |
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| Mathematica Scandinavica 96 (2005) 307-319 |
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| Estimations des Solutions de l'équation de Bezout dans les Algèbres de Beurling analytiques |
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| Mohamed Zarrabi 1Omar El-Fallah |
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| (2005) |
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| 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 $(f_1, ... , f_n)\in A^n$ be such that $\displaystyle \sum _{i=1}^n \|f_i\|^2 \leq 1$. We study here the existence of solutions $(g_1, ... , g_n)\in A^n$ to the Bezout equation $f_1g_1+ ... +f_ng_n=e$, whose norm is controlled by a function of $n$ and $\delta=\inf_{\chi\in\hat A}\left(|\hat f_1(\chi)|^2+...+|\hat f_n(\chi)|^2\right)^{1/2}$. \par 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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| 1: | Institut de Mathématiques de Bordeaux (IMB) |
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CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II |
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| Subject | : | Mathematics/Functional Analysis |
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| Algèbres de Banach – Estimation de la norme d'inverses – Equation de Bezout. |
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| hal-00288491, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00288491 | |
| oai:hal.archives-ouvertes.fr:hal-00288491 | |
| From: Mohamed Zarrabi | |
| Submitted on: Tuesday, 17 June 2008 11:27:11 | |
| Updated on: Tuesday, 17 June 2008 11:27:11 | |
