Let $${ \rm I\!K}$$ be an ultrametric complete valued field and $${ \rm I\!E}$$ be an ultrametric space. We examine some Banach algebras $$S$$ of bounded continuous functions from $${ \rm I\!E}$$ to $${ \rm I\!K}$$ with the use of ultrafilters, particularly the relation of stickness. We recall and deepen results obtained in a previous paper by N. Mainetti and the third author concerning the whole algebra $$\cal A$$ of all bounded continuous functions from $${ \rm I\!E}$$ to $${ \rm I\!K}$$ . Every maximal ideal of finite codimension of $$\cal A$$ is of codimension $$1$$ and we show that this property also holds for every algebra $$S$$ , provided $${ \rm I\!K}$$ is perfect. If $$S$$ admits the uniform norm on $${ \rm I\!E}$$ as its spectral norm, then every maximal ideal is the kernel of only one multiplicative semi-norm, the Shilov boundary is equal to the whole multiplicative spectrum and the Banaschewski compactification of $${ \rm I\!E}$$ is homeomorphic to the multiplicative spectrum of $$S$$ .

中文翻译：

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超度量连续函数的巴拿赫代数的调查和新结果

令 $${ \rm I\!K}$$ 是一个超度量完全值域，$${ \rm I\!E}$$ 是一个超度量空间。我们使用超滤器检查了从 $${ \rm I\!E}$$ 到 $${ \rm I\!K}$$ 的有界连续函数的一些 Banach 代数 $$S$$，特别是粘性。我们回忆并深化了 N. Mainetti 和第三作者在先前论文中获得的结果，涉及从 $${ \rm I\!E}$$ 到 $$ 的所有有界连续函数的整个代数 $$\cal A$$ { \rm I\!K}$$ 。$$\cal A$$ 的有限余维的每个极大理想都是余维 $$1$$ 并且我们证明这个性质也适用于每个代数 $$S$$ ，条件是 $${ \rm I\!K}$ $ 是完美的。如果 $$S$$ 承认 $${ \rm I\!E}$$ 上的一致范数作为它的谱范数，那么每个极大理想只是一个乘法半范数的核，