Ellipsoidal cones in normed vector spaces

الأصل · EN

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 (Jerónimo-Castro and McAllister, 2013).