Work

Polyhedrality and Decomposition

Year: 2018

Type: article

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.

Source: The Quarterly Journal of Mathematics

DOI: 10.1093/qmath/hay050

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