Remarks and examples concerning distance ellipsoids

Dirk Praetorius. "Remarks and examples concerning distance ellipsoids." Colloquium Mathematicae 93.1 (2002): 41-53. <http://eudml.org/doc/285039>.

@article{DirkPraetorius2002,
abstract = {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 $B_E$. 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.},
author = {Dirk Praetorius},
journal = {Colloquium Mathematicae},
keywords = {John ellipsoid; Loewner ellipsoid; ellipsoids; Banach-Mazur distance},
language = {eng},
number = {1},
pages = {41-53},
title = {Remarks and examples concerning distance ellipsoids},
url = {http://eudml.org/doc/285039},
volume = {93},
year = {2002},
}

TY - JOUR
AU - Dirk Praetorius
TI - Remarks and examples concerning distance ellipsoids
JO - Colloquium Mathematicae
PY - 2002
VL - 93
IS - 1
SP - 41
EP - 53
AB - 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 $B_E$. 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.
LA - eng
KW - John ellipsoid; Loewner ellipsoid; ellipsoids; Banach-Mazur distance
UR - http://eudml.org/doc/285039
ER -