Rethinking polyhedrality for Lindenstrauss spaces

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

Research output: Contribution to journalArticlepeer-review

7 Citations (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.
Original languageEnglish
Pages (from-to)355-369
Number of pages15
JournalIsrael Journal of Mathematics
Volume216
DOIs
Publication statusPublished - 2016

Keywords

  • Lindenstrauss space
  • Polyhedrality

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