Uniform dentability, uniform smoothability and approximations to convex sets
type: Item
instance of: scholarly article
title: Uniform dentability, uniform smoothability and approximations to convex sets
zbMATH Open document ID: 0797.46014
author: Daryl Tingley
published in: Rocky Mountain Journal of Mathematics
publication date: 1993-06-29T00:00:00Z
review text: The author defines the notions of uniform dentability and uniform smoothability for a Banach space \(X\) and also gives their weak\(^*\) versions. Proving several technically involved lemmas, it is shown that \(X\) is uniformly (resp. \(X^*\) is weak\(^*\) uniformly) dentable if and only if \(X^*\) is weak\(^*\) uniformly smoothable (resp. \(X\) is uniformly smoothable).
Mathematics Subject Classification ID: 46B22
zbMATH DE Number: 219353
zbMATH Keywords: uniform dentability
zbMATH Keywords: uniform smoothability
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072674
OpenAlex ID: W1997869786
cites work: Smoothability, Strong Smoothability and Dentability in Banach Spaces1
cites work: Q3213662
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cites work: Uniform convexity properties of norms on a super-reflexive Banach space
cites work: A note on smoothability in Banach spaces
cites work: Dentability and extreme points in Banach spaces
cites work: Q5614933
cites work: Martingale proofs of some geometrical results in Banach space theory
DOI: 10.1216/RMJM/1181072674
description: scientific article; zbMATH DE number 219353