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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{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 -