Polyhedrality and decomposition

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

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Polyhedrality and decomposition

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arxiv 1804.06348 v1 pith:Y7MX4SC2 submitted 2018-04-17 math.FA

Polyhedrality and decomposition

Trond A. Abrahamsen , Vladimir P. Fonf , Richard J. Smith , Stanimir Troyanski This is my paper

classification math.FA

keywords banachbasiscertainequivalenthavingnormspolyhedralresults

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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.

Polyhedrality and decomposition

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