Geodesic
New Examples of Non-Archimedean Banach Spaces and Applications
Canadian mathematical bulletin, Tome 55 (2012) no. 4, pp. 821-829

Voir la notice de l'article provenant de la source Cambridge University Press

The study carried out in this paper about some new examples of Banach spaces, consisting of certain valued fields extensions, is a typical non-archimedean feature. We determine whether these extensions are of countable type, have $t$ -orthogonal bases, or are reflexive. As an application we construct, for a class of base fields, a norm $\left\| \,.\, \right\|$ on ${{c}_{0}}$ , equivalent to the canonical supremum norm, without non-zero vectors that are $\left\| \,.\, \right\|$ -orthogonal and such that there is a multiplication on ${{c}_{0}}$ making $\left( {{c}_{0}},\,\left\| \,.\, \right\| \right)$ into a valued field.
DOI : 10.4153/CMB-2011-133-2
Mots-clés : 46S10, 12J25, non-archimedean Banach spaces, valued field extensions, spaces of countable type, orthogonal bases 
Perez-Garcia, C.; Schikhof, W. H. New Examples of Non-Archimedean Banach Spaces and Applications. Canadian mathematical bulletin, Tome 55 (2012) no. 4, pp. 821-829. doi: 10.4153/CMB-2011-133-2
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