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arXiv · 1804.06348

Polyhedrality and decomposition

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

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Trond A. Abrahamsen, Vladimir P. Fonf, Richard J. Smith, Stanimir Troyanski. 2018-04-17. Polyhedrality and decomposition. https://doi.org/10.1093/qmath/hay050

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