Structure of strongly proximinal subspaces

In this paper we extended some results of G. Godefroy, originally proved for c0 using its special geometry, to the class of complex Banach spaces X whose dual is isometric to L1(μ). We exhibit classes of complex Banach spaces in which every strongly proximinal finite codimensional subspace is a fini...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 539; no. 2; p. 128540
Main Author Rao, T.S.S.R.K.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.11.2024
Subjects
[formula omitted]-algebras
[formula omitted]-predual spaces
Strong proximinality
Strong subdifferentiability of the norm
Strong subdifferentiability of the norm
Strong proximinality
L1-predual spaces
C⁎-algebras
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Summary:In this paper we extended some results of G. Godefroy, originally proved for c0 using its special geometry, to the class of complex Banach spaces X whose dual is isometric to L1(μ). We exhibit classes of complex Banach spaces in which every strongly proximinal finite codimensional subspace is a finite dimensional perturbation of a M-ideal. We also show for this class, when the unit ball has an extreme point, if every proximinal subspace of codimension one is strongly proximinal, then the space is isometric to the k-dimensional space with the maximum norm, ℓ∞(k).
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2024.128540