Ellipsoidal cones in normed vector spaces

Farhad Jafari, Tyrrell B. McAllister

Research output: Contribution to journalArticlepeer-review

Abstract

The characterization of ellipsoids is intimately tied to characterizing the Banach spaces that are Hilbert spaces. We give two characterizations of cones over ellipsoids in real normed vector spaces. Let C be a closed convex cone with nonempty interior such that C has a bounded section of codimension 1. We show that C is a cone over an ellipsoid if and only if every bounded section of C has a center of symmetry. We also show that C is a cone over an ellipsoid if and only if the affine span of ∂C ∩ ∂(a - C) has codimension 1 for every point a in the interior of C. These results generalize the finite-dimensional cases proved in [4].

Original languageEnglish (US)
JournalJournal of Convex Analysis
Volume24
Issue number3
StatePublished - Jan 1 2017
Externally publishedYes

Keywords

  • Centrally symmetric convex body
  • Ellipsoidal cone
  • Ordered normed linear space

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