Characterisation of the Berkovich spectrum of the Banach algebra of bounded continuous functions
Tomoki Mihara
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Abstract
For a complete valuation field and a topological space , we prove the universality of the underlying topological space of the Berkovich spectrum of the Banach -algebra of bounded continuous -valued functions on . 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 of , and non-Archimedean Gel'fand theory.
Cite this article
Tomoki Mihara, Characterisation of the Berkovich spectrum of the Banach algebra of bounded continuous functions. Doc. Math. 19 (2014), pp. 769–799
DOI 10.4171/DM/463