CHARACTERISATION OF THE BERKOVICH SPECTRUM OF THE BANACH ALGEBRA OF BOUNDED CONTINUOUS FUNCTIONS

被引：0

作者：

Mihara, Tomoki

机构：

来源：

DOCUMENTA MATHEMATICA | 2014年 / 19卷

关键词：

Berkovich spectrum; Stone space; Banaschewski compactification; non-Archimedean Gel'fand-Naimark theorem; non-Archimedean Gel'fand theory; non-Archimedean Kaplansky conjecture;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 C-bd (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, and non-Archimedean Gel'fand theory.

引用

页码：769 / 799

页数：31