Reflexive extended locally convex spaces

For an extended locally convex space (elcs) (X,τ), the authors in [9] studied the topology τucb of uniform convergence on bounded subsets of (X,τ). In the present paper, we use the topology τucb to explore the reflexive property of extended locally convex spaces. As a main result, we show that an el...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 540; no. 1; p. 128559
Main Authors Kumar, Akshay, Jindal, Varun
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.12.2024
Subjects
Extended locally convex space
Extended normed space
Reflexive spaces
Strong topology
Weak topology
Weak topology
Weak⁎ topology
Strong topology
Extended normed space
Extended locally convex space
Reflexive spaces
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Summary:For an extended locally convex space (elcs) (X,τ), the authors in [9] studied the topology τucb of uniform convergence on bounded subsets of (X,τ). In the present paper, we use the topology τucb to explore the reflexive property of extended locally convex spaces. As a main result, we show that an elcs is (semi) reflexive if and only if any of its open subspaces is (semi) reflexive. For an extended normed space, we show that reflexivity is a three-space property.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2024.128559