Almost flat locally finite coverings of the sphere
type: Item
instance of: scholarly article
title: Almost flat locally finite coverings of the sphere
zbMATH Open document ID: 1075.46012
author: Clemente Zanco
author: V. P. Fonf
published in: Positivity
publication date: 2005-03-15T00:00:00Z
review text: Loosely speaking, a subset of the unit sphere of a Banach space is called flat if its corresponding set of support functionals has small diameter. This concept is naturally connected with subdifferentials of the norm. The main result is that a Banach space has separable dual if and only if it can be renormed so that its new unit sphere admits a countable locally finite tiling by uniformly flat sets. For bigger Banach spaces, the existence of a similar covering is equivalent to the gap between Gâteaux and Fréchet smoothness of the norm.
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46B26
zbMATH DE Number: 2145885
zbMATH Keywords: tiling
zbMATH Keywords: \(\varepsilon\)-flat set
zbMATH Keywords: locally finite covering
zbMATH Keywords: duality mapping
MaRDI profile type: Publication
full work available at URL: s11117-004-5036-6
OpenAlex ID: W2026590293
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DOI: 10.1007/S11117-004-5036-6
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description: scientific article; zbMATH DE number 2145885