Reflexive extended locally convex spaces
type: Item
instance of: scholarly article
title: Reflexive extended locally convex spaces
author: Q6050657
author: Varun Jindal
published in: Journal of Mathematical Analysis and Applications
publication date: 2024-09-18T00:00:00Z
review text: The authors continue their investigation of extended locally convex spaces (elcs) in the sense of \textit{D.~Salas} and \textit{S.~Tapia-García} [Topology Appl. 210, 317--354 (2016; Zbl 1359.46003)]. Here, they use the topology \(\tau_{ucb}\) of uniform convergence on bounded subsets of an elcs \((X,\tau)\) to explore its reflexivity property. In particular, they show that an elcs is (semi) reflexive if and only if its open subspaces are (semi) reflexive. Moreover, it is shown that reflexivity of extended normed spaces is a three-space property.
reviewed by: Zoran Kadelburg
Mathematics Subject Classification ID: 46A25
Mathematics Subject Classification ID: 46B10
zbMATH DE Number: 7915149
zbMATH Keywords: extended locally convex space
zbMATH Keywords: extended normed space
zbMATH Keywords: topology of uniform convergence
zbMATH Keywords: reflexive spaces
zbMATH Keywords: three-space property
MaRDI profile type: Publication
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DOI: 10.1016/J.JMAA.2024.128559
description: scientific article; zbMATH DE number 7915149