Characterisation of the Berkovich spectrum of the Banach algebra of bounded continuous functions
Characterisation of the Berkovich spectrum of the Banach algebra of bounded continuous functions
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DOI：
10.4171/dm/463
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发表时间：
2013-03
影响因子：
0.9
通讯作者：
Tomoki Mihara
中科院分区：
文献类型：
--
作者：
Tomoki Mihara
对于完全赋值域k和拓扑空间X，我们证明了X上有界连续k值函数的Banach k代数Cbd（X, k）的Berkovich谱底层拓扑空间的通用性。这一结果给出了三个应用：局部域上自动连续性问题的Kaplansky猜想的一个模拟的部分解，Cbd（X, k）的两个地面域扩展的比较，以及非阿基米德Gel'fand理论。关键词：Berkovich谱，Stone空间，Banaschewski紧化，非阿基米德Gel’fand- naimark theo rem，非阿基米德Gel’fand理论，非阿基米德Kaplansky猜想
For a complete valuation field k and a topological space X, we prove the universality of the underlying topological space of the Berkovich spectrum of the Banach k-algebra Cbd(X, k) of bounded continuous k-valued functions on X. This result yields three applications: a partial solution to an analogue of Kaplansky conjecture for the automatic continuity problem over a local field, comparison of two ground field extensions o f Cbd(X, k), and non-Archimedean Gel'fand theory. 2010 Mathematics Subject Classification: 11S80, 18B30, 46S 10 Keywords and Phrases: Berkovich spectrum, Stone space, Banaschewski compactification, non-Archimedean Gel'fand-Naimark theo rem, non- Archimedean Gel'fand theory, non-Archimedean Kaplansky conjecture