On linearisation, existence and uniqueness of preduals: the isometric case
Citation Link: https://doi.org/10.15480/882.17508
Publikationstyp
Journal Article
Date Issued
2026-07-14
Sprache
English
Author(s)
TORE-DOI
Volume
20
Issue
3
Start Page
1
End Page
23
Article Number
40
Citation
Banach Journal of Mathematical Analysis 20 (3): 23-40 (2026)
Publisher DOI
Scopus ID
ArXiv ID
Publisher
Springer
Peer Reviewed
true
We study the problem of existence and uniqueness of isometric Banach preduals of a Banach space. We derive necessary and sufficient conditions for the existence of an isometric Banach predual of a Banach space X. Then we focus on the case that X = F(Ω) is a Banach space of scalar-valued functions on a non-empty set Ω and describe those spaces which admit a special isometric Banach predual, namely a strong isometric Banach linearisation, i.e. there are a Banach space Y , a map δ∶Ω → Y and an isometric isomorphism T∶F(Ω) → Y* such that T(f)○δ = f for all f ∈ F(Ω). Finally, we give necessary and sufficient conditions for Banach spaces F(Ω) with a strong isometric Banach linearisation to have a (strongly) unique isometric Banach predual.
Subjects
dual space
predual
linearisation
uniqueness
isometric
Saks space
DDC Class
515: Analysis
Publication version
publishedVersion