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

Enrico Miglierina, Emanuele Casini, Łukasz Piasecki

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

## 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.
Original language English 459-470 12 Canadian Mathematical Bulletin 58 https://doi.org/10.4153/CMB-2015-024-9 Published - 2015

## Keywords

• $\ell_1$-predual
• hyperplane
• projections
• space of convergent sequences

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