Rethinking polyhedrality for Lindenstrauss spaces

Enrico Miglierina, Lukasz Piasecki, Emanuele Casini, Łukasz Piasecki, Libor Veselý

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

6 Citazioni (Scopus)

Abstract

We present a Lindenstrauss space with an extreme point that does not contain a subspace linearly isometric to c. This example disproves a re- sult stated by Zippin in a paper published in 1969 and it shows that some classical characterizations of polyhedral Lindenstrauss spaces, based on Zippin’s result, are false, whereas some others remain unproven; then we provide a correct proof for those characterizations. Finally, we also disprove a characterization of polyhedral Lindenstrauss spaces given by Lazar, in terms of the compact norm-preserving extension of compact op- erators, and we give an equivalent condition for a Banach space X to satisfy this property.
Lingua originaleEnglish
pagine (da-a)355-369
Numero di pagine15
RivistaIsrael Journal of Mathematics
Volume216
DOI
Stato di pubblicazionePubblicato - 2016

Keywords

  • Lindenstrauss space
  • Polyhedrality

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