The Mackey- Ulam theorem in topological vector spaces
type: Item
instance of: scholarly article
title: The Mackey- Ulam theorem in topological vector spaces
zbMATH Open document ID: 0818.46003
DOI: 10.1007/BF01258060
published in: Archiv der Mathematik
publication date: 1993-11-15T00:00:00Z
review text: A topological vector space \(E\) is called \({\mathcal L}\)-bornological, if every bounded linear map from \(E\) into any topological vector space \(F\) is continuous. The author proves that a product \(\prod_{\alpha\in I} E_ \alpha\) of arbitrary \({\mathcal L}\)-bornological spaces is again \({\mathcal L}\)-bornological iff the locally convex space \(\omega(I)\) of all functions from \(I\) to \(\mathbb{R}\) (or \(\mathbb{C}\)) is bornological in the locally convex sense. This is the case if the cardinality of the index set \(I\) is smaller than the smallest strongly non accessible cardinal number [see \S28 (8) in \textit{G. Köthe}: `Topologische lineare Räume. I' (1966; Zbl 0137.313)].
Mathematics Subject Classification ID: 46A08
Mathematics Subject Classification ID: 46A16
zbMATH DE Number: 446298
zbMATH Keywords: Mackey-Ulam theorem
zbMATH Keywords: product
zbMATH Keywords: \({\mathcal L}\)-bornological spaces
author: Norbert Adasch
reviewed by: Winfried Kaballo
MaRDI profile type: Publication
cites work: Topologische Produkte gewisser topologischer Vektorräume
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cites work: Q5723419
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description: scientific article; zbMATH DE number 446298