Remarks and examples concerning distance ellipsoids

• Autorzy: Dirk Praetorius
• Języki publikacji: EN

Abstrakty

EN

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

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B04: Isometric theory of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2002
• Tom: 93
• Numer: 1
• Strony: 41-53

Daty

wydano

2002

Twórcy

autor

Dirk Praetorius

• Institute for Applied Mathematics and Numerical Analysis, Vienna University of Technology, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria

Identyfikatory

DOI

10.4064/cm93-1-5