01-1   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Dirk Praetorius:

Remarks And Examples Concerning Distance Ellipsoids

We provide and examine examples of finite dimensional Banach spaces with non-unique distance ellipsoid. The main result is the construction of an n-dimensional Banach space E such that there are precisely k linearly independent contact points between the unit ball and the unique distance ellipsoid of E, where 2 <= k <= n is arbitrary. Further, the corresponding result is shown for spaces with non-unique distance ellipsoid.

Mathematics Subject Classification (1991): 46B04, 46B20

Bibliographical note: Angenommen bei Colloquium Mathematicum

Keywords: ellipsoids, John ellipsoid, Loewner ellipsoid, Banach-Mazur distance


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[Thu Feb 19 18:56:35 2009]
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