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arXiv · 1501.07493

Ellipsoidal cones in normed vector spaces

Farhad Jafari·Tyrrell B. McAllister
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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 (Jerónimo-Castro and McAllister, 2013).

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Farhad Jafari, Tyrrell B. McAllister. 2015-01-29. Ellipsoidal cones in normed vector spaces. https://arxiv.org/abs/1501.07493

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