Geodesic
Remarks and examples concerning distance ellipsoids
Dirk Praetorius1
1 Institute for Applied Mathematics and Numerical Analysis Vienna University of Technology Wiedner Hauptstrasse 8-10 A-1040 Wien, Austria
Colloquium Mathematicum, Tome 93 (2002) no. 1, pp. 41-53.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We provide for every $2\le k\le n$ an $n$-dimensional Banach space $E$ with a unique distance ellipsoid ${\cal E}$ such that there are precisely $k$ linearly independent contact points between ${\cal E}$ 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.
DOI : 10.4064/cm93-1-5
Keywords: provide every n dimensional banach space unique distance ellipsoid cal there precisely linearly independent contact points between cal corresponding result holds spaces non unique distance ellipsoids construct n dimensional banach spaces distance ellipsoid has precisely linearly independent contact points other distance ellipsoids have k points

Dirk Praetorius 1

1 Institute for Applied Mathematics and Numerical Analysis Vienna University of Technology Wiedner Hauptstrasse 8-10 A-1040 Wien, Austria 
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Dirk Praetorius. Remarks and examples concerning
 distance ellipsoids. Colloquium Mathematicum, Tome 93 (2002) no. 1, pp. 41-53. doi : 10.4064/cm93-1-5. http://geodesic.mathdoc.fr/articles/10.4064/cm93-1-5/

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