The Dvoretzky-Hanani lemma for rectangles
type: Item
instance of: scholarly article
title: The Dvoretzky-Hanani lemma for rectangles
zbMATH Open document ID: 0849.52001
DOI: 10.1007/BF01876346
author: Wojciech Banaszczyk
published in: Periodica Mathematica Hungarica
publication date: 1996-11-05T00:00:00Z
review text: For symmetric convex bodies \(U,V\) in the plane, \(\sigma (U,V)\) is the smallest positive number \(r\) such that for any finite sequence \(u_1, \dots, u_n \in U\) there are signs \(\varepsilon_i\) with \(\varepsilon_1 u_1 + \cdots + \varepsilon_k u_k \in r^V\) for \(k = 1, \dots, n\). Those rectangles \(R\) with sides parallel to the coordinate axes are characterized for which \(\sigma (K,R) \leq 1\), where \(K\) is the unit ball of the maximum norm. It is mentioned that there is a relation to rearrangements of series in locally convex spaces.
Mathematics Subject Classification ID: 52A10
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 52C99
Mathematics Subject Classification ID: 46A03
zbMATH DE Number: 894303
zbMATH Keywords: rectangles
zbMATH Keywords: rearrangements of series
reviewed by: Erhard Heil
MaRDI profile type: Publication
Wikidata QID: Q124979043
cites work: Additive subgroups of topological vector spaces
cites work: The Steinitz lemma in \(\ell^ 2_{\infty{}}\)
cites work: Balancing families of integer sequences
cites work: Q5785210
description: scientific article; zbMATH DE number 894303