Polyhedrality in pieces

V. Fonf, A. J. Pallarés, R. J. Smith, S. Troyanski

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

The aim of this paper is to present two tools, Theorems 4 and 7, that make the task of finding equivalent polyhedral norms on certain Banach spaces easier and more transparent. The hypotheses of both tools are based on countable decompositions, either of the unit sphere SX or of certain subsets of the dual ball BX* of a given Banach space X. The sufficient conditions of Theorem 4 are shown to be necessary in the separable case. Using Theorem 7, we can unify two known results regarding the polyhedral renorming of certain C(K) spaces, and spaces having an (uncountable) unconditional basis. New examples of spaces having equivalent polyhedral norms are given in the final section.

Original languageEnglish
Pages (from-to)247-264
Number of pages18
JournalJournal of Functional Analysis
Volume266
Issue number1
DOIs
StatePublished - 1 Jan 2014

Keywords

  • Boundaries
  • Countable covers
  • Polyhedral norms and renormings
  • Polytopes

ASJC Scopus subject areas

  • Analysis

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