Topology Proceedings
Document # baak-30
Electronic Version 24 Summer (1999) |
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Banach spaces over nonarchimedean valued fields
Wim H. Schikhof
In this survey note we present the state of the art on the theory of Banach and Hilbert spaces over complete valued scalar fields that are not isomorphic to R or C. For convenience we treat `classical' theorems (such as Hahn-Banach Theorem, Closed Range Theorem, Riesz Representation Theorem, Eberlein-mulian's Theorem, Krein-Milman Theorem) and discuss whether or not they remain valid in this new context, thereby stating sometimes strong negations or strong improvements. Meanwhile several concepts are being introduced (such as norm orthogonality, spherical completeness, compactoidity, modules over valuation rings) leading to results that do not have - or at least have less important - counterparts in the classical theory.
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Topology Proceedings Electronic Version
Copyright © 2001
Nipissing University
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Date published electronically: March 5, 2001.