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New Examples of Non-Archimedean Banach Spaces and Applications

Published online by Cambridge University Press:  20 November 2018

C. Perez-Garcia  and
W. H. Schikhof
C. Perez-Garcia
Affiliation:
Department of Mathematics, Facultad de Ciencias, Universidad de Cantabria, 39071 Santander, Spaine-mail: perezmc@unican.es
W. H. Schikhof
Affiliation:
Department of Mathematics, Radboud University, 6525 ED Nijmegen, The Netherlandse-mail: w_schikhof@hetnet.nl
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Abstract

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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.

Keywords

46S1012J25non-archimedean Banach spacesvalued field extensionsspaces of countable typeorthogonal bases
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 4 , 01 December 2012 , pp. 821 - 829
Copyright
Copyright © Canadian Mathematical Society 2012

References

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