Minimal-volume shadows of cubes
type: Item
instance of: scholarly article
title: Minimal-volume shadows of cubes
zbMATH Open document ID: 0968.46017
published in: Journal of Functional Analysis
publication date: 2000-11-14T00:00:00Z
review text: A proof is given that for every subspace \(L\) of \(\mathbb{R}^m\), the set of minimal-volume shadows in \(L\) contains a parallelepiped. The main result is that for some subspaces there exist minimal-volume shadows that are far from parallelepipeds with respect to the Banach-Mazur distance.
reviewed by: Joe Howard
Mathematics Subject Classification ID: 46B20
zbMATH DE Number: 1529987
zbMATH Keywords: minimal-volume shadows
zbMATH Keywords: parallelepiped
zbMATH Keywords: parallelepipeds
zbMATH Keywords: Banach-Mazur distance
author: Mikhail Ostrovskii
MaRDI profile type: Publication
full work available at URL: jfan.2000.3641
OpenAlex ID: W2092796881
cites work: Q5775371
cites work: Open problems of Paul Erd�s in graph theory
cites work: Eigenvalues of Graphs and Sobolev Inequalities
cites work: Banach ideals on Hilbert spaces
cites work: Ratios of volumes and factorization through \(\ell_ \infty\)
cites work: Q3239535
cites work: Sobolev imbedding operators and the nonisomorphism of certain Banach spaces
cites work: Absolutely summing operators in $ℒ_{p}$-spaces and their applications
cites work: Projections in normed linear spaces and sufficient enlargements
cites work: Q3715635
cites work: Q3036193
cites work: Q3818127
cites work: Combinatorial Properties of Associated Zonotopes
cites work: Q4041061
DOI: 10.1006/JFAN.2000.3641
description: scientific article; zbMATH DE number 1529987