Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-12-01T10:30:27.794Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
W. H. Schikhof
Affiliation:
Department of Mathematics, Radboud University, 6525 ED Nijmegen, The Netherlandse-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1] Robert, A. M., A Course in p-Adic Analysis. Graduate Texts in Mathematics,198. Springer-Verlag, New York, 2000.Google Scholar
[2] van Rooij, A. C. M., Non-Archimedean Functional Analysis. Monographs and Textbooks in Pure and Applied Math. 51. Marcel Dekker, New York, 1978.Google Scholar
[3] Schikhof, W. H., Ultrametric Calculus. An Introduction to p-Adic Analysis. Cambridge Studies in Advanced Mathematics 4. Cambridge University Press, Cambridge, 1984.Google Scholar