Geodesic
Hyperplanes in the Space of Convergent Sequences and Preduals of l1
Canadian mathematical bulletin, Tome 58 (2015) no. 3, pp. 459-470

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DOI

The main aim of this paper is to investigate various structural properties of hyperplanes of $c$ , the Banach space of the convergent sequences. In particular, we give an explicit formula for the projection constants and prove that an hyperplane of $c$ is isometric to the whole space if and only if it is 1-complemented. Moreover, we obtain the classification of those hyperplanes for which their duals are isometric to ${{\ell }_{1}}$ and give a complete description of the preduals of ${{\ell }_{1}}$ under the assumption that the standard basis of ${{\ell }_{1}}$ is weak $^{*}$ -convergent.
DOI : 10.4153/CMB-2015-024-9
Mots-clés : 46B45, 46B04, space of convergent sequences, projection, l1-predual, hyperplane 
Casini, Emanuele; Miglierina, Enrico; Piasecki, Łukasz. Hyperplanes in the Space of Convergent Sequences and Preduals of l1. Canadian mathematical bulletin, Tome 58 (2015) no. 3, pp. 459-470. doi: 10.4153/CMB-2015-024-9
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     author = {Casini, Emanuele and Miglierina, Enrico and Piasecki, {\L}ukasz},
     title = {Hyperplanes in the {Space} of {Convergent} {Sequences} and {Preduals} of l1},
     journal = {Canadian mathematical bulletin},
     pages = {459--470},
     year = {2015},
     volume = {58},
     number = {3},
     doi = {10.4153/CMB-2015-024-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-024-9/}
}
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%J Canadian mathematical bulletin
%D 2015
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