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 languageEnglish
Pages (from-to)459-470
Number of pages12
JournalCanadian Mathematical Bulletin
Volume58
DOIs
Publication statusPublished - 2015

Keywords

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

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