This is an announcement for the paper "Ellipsoidal cones in normed vector spaces" by Farhad Jafari and Tyrrell B. McAllister.
Abstract: 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 $\partial C \cap \partial(a - C)$ has codimension $1$ for every point $a$ in the interior of $C$. These results generalize the finite-dimensional cases proved in (Jer'onimo-Castro and McAllister, 2013).
Archive classification: math.FA math.MG
Mathematics Subject Classification: Primary 46B20, Secondary 52A50, 46B40, 46B10
Remarks: 10 pages, 1 figure
Submitted from: tmcallis@uwyo.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1501.07493
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