POLYHEDRALITY and DECOMPOSITION

Trond A. Abrahamsen, Vladimir P. Fonf, Richard J. Smith, Stanimir Troyanski

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The aim of this note is to present two results that make the task of finding equivalent polyhedral norms on certain Banach spaces, having either a Schauder basis or an uncountable unconditional basis, easier and more transparent. The hypotheses of both results are based on decomposing the unit sphere of a Banach space into countably many pieces, such that each one satisfies certain properties. Some examples of spaces having equivalent polyhedral norms are given.

Original languageEnglish
Article numberhay050
Pages (from-to)409-427
Number of pages19
JournalQuarterly Journal of Mathematics
Volume70
Issue number2
DOIs
StatePublished - 13 Jun 2019

ASJC Scopus subject areas

  • General Mathematics

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