The main aim of the present 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 we 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 we give a complete description of the preduals of under the assumption that the standard basis of $\ell_1$ is weak^*-convergent.

Casini, E., Miglierina, E., Piasecki, L., Hyperplanes in the space of convergent sequences and preduals of $\ell_1$, <<CANADIAN MATHEMATICAL BULLETIN>>, 2015; 58 (3): 459-470. [doi:10.4153/CMB-2015-024-9] [http://hdl.handle.net/10807/65810]

### Hyperplanes in the space of convergent sequences and preduals of $\ell_1$

#### Abstract

The main aim of the present 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 we 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 we give a complete description of the preduals of under the assumption that the standard basis of $\ell_1$ is weak^*-convergent.
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Casini, E., Miglierina, E., Piasecki, L., Hyperplanes in the space of convergent sequences and preduals of $\ell_1$, <<CANADIAN MATHEMATICAL BULLETIN>>, 2015; 58 (3): 459-470. [doi:10.4153/CMB-2015-024-9] [http://hdl.handle.net/10807/65810]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/65810
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