Non-archimedean Eberlein-Šmulian theory
type: Item
instance of: scholarly article
title: Non-archimedean Eberlein-Šmulian theory
zbMATH Open document ID: 0856.46051
DOI: 10.1155/S0161171296000907
author: Takemitsu Kiyosawa
author: Wim Schikhof
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1996-09-30T00:00:00Z
full work available at URL: https://eudml.org/doc/47586
review text: Summary: It is shown that, for a large class of non-Archimedean normed spaces \(E\), a subset \(X\) is weakly compact as soon as \(f(X)\) is compact for all \(f\in E'\), a fact that has no analogue in functional analysis over the real or complex numbers. As a corollary, we derive a non-Archimedean version of the Eberlein-Šmulian Theorem.
Mathematics Subject Classification ID: 46S10
Mathematics Subject Classification ID: 46A40
zbMATH DE Number: 930039
zbMATH Keywords: non-Archimedean normed spaces
zbMATH Keywords: weakly compact
zbMATH Keywords: Eberlein-Šmulian Theorem
MaRDI profile type: Publication
OpenAlex ID: W2158810825
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description: scientific article; zbMATH DE number 930039