[Back]

D. Praetorius:
"Remarks and Examples Concerning Distance Ellipsoids";
Colloquium Mathematicum, 93 (2002), 41 - 53.

We provide for every 2<=k<=n an n-dimensional Banach space E with a
unique distance ellipsoid ε such that there are precisely k
linearly independent contact points between ε 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.

http://www.anum.tuwien.ac.at/~dirk/download/preprint/ellipsoid.pdf