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

Voir la notice de l'article provenant de la source Cambridge University Press

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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