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

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.