Remarks and examples concerning distance ellipsoids
Volume 93 / 2002
Colloquium Mathematicum 93 (2002), 41-53
MSC: 46B04, 46B20.
DOI: 10.4064/cm93-1-5
Abstract
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.
