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

Enrico Miglierina, Emanuele Casini, Łukasz Piasecki

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

8 Citazioni (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.
Lingua originaleEnglish
pagine (da-a)459-470
Numero di pagine12
RivistaCanadian Mathematical Bulletin
Volume58
DOI
Stato di pubblicazionePubblicato - 2015

Keywords

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

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