We provide for every 2 ≤ k ≤ n an n-dimensional Banach space E with a unique distance ellipsoid such that there are precisely k linearly independent contact points between and . The corresponding result holds for spaces with non-unique distance ellipsoids as well. We construct n-dimensional Banach spaces E such that one distance ellipsoid has precisely k linearly independent contact points and all other distance ellipsoids have less than k-1 such points.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm93-1-5,
author = {Dirk Praetorius},
title = {Remarks and examples concerning distance ellipsoids},
journal = {Colloquium Mathematicae},
volume = {91},
year = {2002},
pages = {41-53},
zbl = {1017.46006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm93-1-5}
}
Dirk Praetorius. Remarks and examples concerning distance ellipsoids. Colloquium Mathematicae, Tome 91 (2002) pp. 41-53. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm93-1-5/