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On linearization and uniqueness of preduals
Citation Link: https://doi.org/10.15480/882.15380
Publikationstyp
Journal Article
Date Issued
2025-03-01
Sprache
English
Author(s)
TORE-DOI
Journal
Volume
298
Issue
3
Start Page
955
End Page
975
Citation
Mathematische Nachrichten 298 (3): 955-975 (2025)
Publisher DOI
Scopus ID
ArXiv ID
Publisher
Wiley
Peer Reviewed
true
We study strong linearizations and the uniqueness of preduals of locally convex Hausdorff spaces of scalar-valued functions. Strong linearizations are special preduals. A locally convex Hausdorff space (Formula presented.) of scalar-valued functions on a nonempty set (Formula presented.) is said to admit a strong linearization if there are a locally convex Hausdorff space (Formula presented.), a map (Formula presented.), and a topological isomorphism (Formula presented.) such that (Formula presented.) for all (Formula presented.). We give sufficient conditions that allow us to lift strong linearizations from the scalar-valued to the vector-valued case, covering many previous results on linearizations, and use them to characterize the bornological spaces (Formula presented.) with (strongly) unique predual in certain classes of locally convex Hausdorff spaces.
Subjects
dual space | linearization | predual | uniqueness
DDC Class
515: Analysis
510: Mathematics
Publication version
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