arXiv 1804.063482018-04-17math.FA

Polyhedrality and decomposition

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

DOI：: 10.1093/qmath/hay050

英文摘要：

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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