Geodesic
Characterisation of the Berkovich spectrum of the Banach algebra of bounded continuous functions
Documenta mathematica, Tome 19 (2014), pp. 769-799
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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.
DOI : 10.4171/dm/463
Classification : 11S80, 46S10
Mots-clés : berkovich spectrum, stone space, banaschewski compactification, non-Archimedean Gelfand--Naimark theorem, non-Archimedean Gelfand theory, non-Archimedean Kaplansky conjecture 
@article{10_4171_dm_463,
     author = {Tomoki Mihara},
     title = {Characterisation of the {Berkovich} spectrum of the {Banach} algebra of bounded continuous functions},
     journal = {Documenta mathematica},
     pages = {769--799},
     year = {2014},
     volume = {19},
     doi = {10.4171/dm/463},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/463/}
}
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Tomoki Mihara. Characterisation of the Berkovich spectrum of the Banach algebra of bounded continuous functions. Documenta mathematica, Tome 19 (2014), pp. 769-799. doi: 10.4171/dm/463

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