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Finite-Dimensional Subspaces of the p-Adic Space ℓ∞

Published online by Cambridge University Press:  20 November 2018

C. Perez-Garcia  and
Wim H. Schikhof
C. Perez-Garcia
Affiliation:
Department of Mathematics, Universidad de Cantabria, Avda de los Castros, 39071 Santander, Spain
Wim H. Schikhof
Affiliation:
Department of Mathematics, University of Nijmegen, Toernooiveld, 6525 ED Nijmegen, The Netherlands
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Abstract

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For finite-dimensional subspaces of ℓ∞ over a non-archimedean valued base field K we study orthocomplementation as related to the Hahn-Banach property and strictness. As a corollary we obtain that, if K is not spherically complete, a closed hyperplane in c0 having the Hahn-Banach property is orthocomplemented (Theorem 2.1, Remark 2).

Keywords

46S10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 3 , 01 September 1995 , pp. 360 - 365
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Perez-Garciaand, C. Schikhof, W. H., p-adic orthocomplementedsubspaces in l∞, Report 9313, Department of Mathematics, Catholic University, Nijmegen, The Netherlands, 1993.Google Scholar
2. C. M. van Rooij, A., Non-Archimedean Functional Analysis, Marcel Dekker, New York, 1978.Google Scholar
3. C. M. van Rooij, A., Notes on p-adic Banach spaces I—V, Report 7633, Department of Mathematics, Catholic University, Nijmegen, The Netherlands, 1976.Google Scholar
4. Schikhof, W. H., More on duality betweenp-adic Banach spaces andcompactoids, Report 9301, Department of Mathematics, Catholic University, Nijmegen, The Netherlands, 1993.Google Scholar