Differential and maximal ideals of the ultrametric Corona algebra

Abstract : Let $K$ be a complete ultrametric algebraically closed field and let $A$ be the Banach $K$-algebra of bounded analytic functions in the ''open'' unit disk $D$ of $K$ provided with the Gauss norm. Maximal ideals of infinite codimension are examined in connection with ultrafilters on $D$. Four classes of ultrafilters on $D$ are considered, defining a null ideal, or a maximal ideal or an unidentified ideal. A function $f\in A$ tends to $0$ along a sequence of disks $|x-a_n|
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Alain Escassut. Differential and maximal ideals of the ultrametric Corona algebra. Contemporary mathematics, American Mathematical Society, 2011, 551, pp.105-116. ⟨hal-00682131⟩

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