Characterisation of the Berkovich Spectrum of the Banach Algebra of Bounded Continuous Functions

Tomoki Mihara

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arXiv · 1303.0397

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 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 of Cbd(X,k), and non-Archimedean Gel'fand theory.

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Tomoki Mihara. 2013-03-02. Characterisation of the Berkovich Spectrum of the Banach Algebra of Bounded Continuous Functions. https://arxiv.org/abs/1303.0397

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