New Examples of Non-Archimedean Banach Spaces and Applications

Canadian mathematical bulletin

C. Perez-Garcia¹  W. H. Schikhof² 

[1] Department of Mathematics, Facultad de Ciencias, Universidad de Cantabria, 39071 Santander, Spain;Department of Mathematics, Radboud University, 6525 ED Nijmegen, The Netherlands

关键词: non-archimedean Banach spaces;    valued field extensions;    spaces of countable type;    orthogonal bases;   

DOI  :  10.4153/CMB-2011-133-2

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

The study carried out in this paper about some new examples ofBanach spaces, consisting of certain valued fields extensions, isa typical non-archimedean feature. We determine whether theseextensions are of countable type, have $t$-orthogonal bases, or arereflexive.As an application we construct, for a class of base fields, a norm $|cdot|$ on $c_0$, equivalent to the canonical supremum norm,without non-zero vectors that are $|cdot|$-orthogonal and suchthat there is a multiplication on $c_0$ making $(c_0,|cdot|)$ into a valued field.

【 授权许可】

Unknown