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

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DOI

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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     title = {New {Examples} of {Non-Archimedean} {Banach} {Spaces} and {Applications}},
     journal = {Canadian mathematical bulletin},
     pages = {821--829},
     year = {2012},
     volume = {55},
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     doi = {10.4153/CMB-2011-133-2},
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