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Nonmaximal ideals and the Berkovich space of the algebra of bounded analytic functions

Abstract: We prove that the Berkovich space (or multiplicative spectrum) of the algebra of bounded analytic functions on the open unit disk of an algebraically closed nonarchimedean field contains multiplicative seminorms that are not norms and whose kernel is not a maximal ideal. We also prove that in general these seminorms are not univocally determined by their kernels, and provide a method for obtaining families of different seminorms sharing the same kernel. The relation with the Berkovich space of the Tate algebra is also given.

 Fuente: Journal of Mathematical Analysis and Applications, Volume 455, Issue 1, 1 November 2017, Pages 221-245

 Editorial: Academic Press Inc.

 Año de publicación: 2017

 Nº de páginas: 25

 Tipo de publicación: Artículo de Revista

 DOI: 10.1016/j.jmaa.2017.05.039

 ISSN: 0022-247X,1096-0813

 Proyecto español: MTM2016-77143-P

 Url de la publicación: https://doi.org/10.1016/j.jmaa.2017.05.039