Minimal-Volume Shadows of Cubes

Minimal-Volume Shadows of Cubes

We study the shape of minimal-volume shadows of a cube in a given subspace. First we prove an essentially known result that for every subspace L the set of minimal-volume shadows in L contains a parallelepiped. Our main result is that for some subspaces there exist minimal-volume shadows that are fa...

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Veröffentlicht in:Journal of functional analysis 2000-10, Vol.176 (2), p.317-330
1. Verfasser: Ostrovskii, M.I.
Format: Artikel
Sprache:eng
Schlagworte:
absolutely summing operator
compound matrix
cube
directed graph
Grothendieck theorem
minimal volume
projection
Sobolev inequality
the Banach–Mazur distance
totally unimodular matrix
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Zusammenfassung:We study the shape of minimal-volume shadows of a cube in a given subspace. First we prove an essentially known result that for every subspace L the set of minimal-volume shadows in L contains a parallelepiped. Our main result is that for some subspaces there exist minimal-volume shadows that are far from parallelepipeds with respect to the Banach–Mazur distance.
ISSN:0022-1236
1096-0783
DOI:10.1006/jfan.2000.3641