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On linearisation and existence of preduals
Citation Link: https://doi.org/10.15480/882.13189
Publikationstyp
Journal Article
Date Issued
2024-06-01
Sprache
English
Author(s)
TORE-DOI
Volume
73
Issue
4
Start Page
1591
End Page
1615
Citation
Rendiconti del Circolo Matematico di Palermo 73 (4): 1591-1615 (2024)
Publisher DOI
Scopus ID
Publisher
Springer Italia
We study the problem of existence of preduals of locally convex Hausdorff spaces. We derive necessary and sufficient conditions for the existence of a predual with certain properties of a bornological locally convex Hausdorff space X. Then we turn to the case that X=F(Ω) is a space of scalar-valued functions on a non-empty set Ω and characterise those among them which admit a special predual, namely a strong linearisation, i.e. there are a locally convex Hausdorff space Y, a map δ:Ω→Y and a topological isomorphism T:F(Ω)→Yb′ such that T(f)∘δ=f for all f∈F(Ω).
Subjects
Dual space
Linearisation
Mixed topology
Predual
DDC Class
510: Mathematics
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Name
s12215-024-01004-8.pdf
Type
Main Article
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Format
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