Differential and maximal ideals of the ultrametric Corona algebra

Alain Escassut (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

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|

Mots clés: p-adic analytic functions; ultrametric corona problem; maximal ideals

Domaines: Théorie des nombres [math.NT]

Alain Escassut. Differential and maximal ideals of the ultrametric Corona algebra. Contemporary mathematics, 2011, 551, pp.105-116. ⟨hal-00682131⟩