This is an announcement for the paper "Hyperplanes in the space of convergent sequences and preduals of $\ell_1$" by E. Casini, E. Miglierina, and L. Piasecki.

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 $\ell_{1}$ under the assumption that the standard basis of $\ell_{1}$ is weak$^{*}$-convergent.

Archive classification: math.FA

Mathematics Subject Classification: 46B45 (Primary), 46B04 (Secondary)

Submitted from: enrico.miglierina@unicatt.it

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1410.7801

or

http://arXiv.org/abs/1410.7801