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- W189891938 abstract "Let $A$ be a unitary commutative Banach algebra with unit $e$. For $fin A$ 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 $delta=inf_{chiinhat A}(|hat f_1(chi)|^2+cdots+|hat f_n(chi)|^2)^{1/2}$. 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." @default.
- W189891938 created "2016-06-24" @default.
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- W189891938 date "2005-06-01" @default.
- W189891938 modified "2023-10-01" @default.
- W189891938 title "Estimations des solutions de l'équation de Bezout dans les algèbres de Beurling analytiques" @default.
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- W189891938 doi "https://doi.org/10.7146/math.scand.a-14959" @default.
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