Abstract
Let K be a non-archimedean valued field whose valuation is complete and nontrivial. It is shown that ℓ∞ is complemented in any polar K-Banach space (Theorem 1.2) which opens the way for various descriptions of complemented subspaces of ℓ∞ (Theorem 2.3).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
N. de Grande-de Kimpe and C. Perez-Garcia: Weakly closed subspaces and the Hahn-Banach extension property in p-adic analysis. Proc. Kon. Ned. Akad. Wet. 91, 253–261 (1988).
A.C.M. van Rooij: Non-archimedean functional analysis. Marcel Dekker, New York (1978).
W.H. Schikhof: Locally convex spaces over nonspherically complete valued fields. Groupe d'étude d'analyse ultramétrique 12 no. 24, 1–33 (1984/85).
W.H. Schikhof: A connection between p-adic Banach spaces and locally convex compactoids. Report 8736, Department of Mathematics, Catholic University, Nijmegen, 1–16 (1987).
J. van Tiel: Espaces localement K-convexes. Indag. Math. 27, 249–289 (1965).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1990 Springer-Verlag
About this chapter
Cite this chapter
Schikhof, W.H. (1990). The complementation property of ℓ∞ in p-adic banach spaces. In: Baldassarri, F., Bosch, S., Dwork, B. (eds) p-adic Analysis. Lecture Notes in Mathematics, vol 1454. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091148
Download citation
DOI: https://doi.org/10.1007/BFb0091148
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53477-8
Online ISBN: 978-3-540-46906-3
eBook Packages: Springer Book Archive