
Journal of Convex Analysis 24 (2017), No. 3, 795805 Copyright Heldermann Verlag 2017 Ellipsoidal Cones in Normed Vector Spaces Farhad Jafari Dept. of Mathematics, University of Wyoming, Laramie, WY 82071, U.S.A. fjafari@uwyo.edu Tyrrell B. McAllister Dept. of Mathematics, University of Wyoming, Laramie, WY 82071, U.S.A. tmcallis@uwyo.edu [Abstractpdf] 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 $\partial C \cap \partial(a  C)$ has codimension $1$ for every point $a$ in the interior of $C$. These results generalize the finitedimensional cases proved by J. Jer{\'o}nimoCastro and T. B. McAllister [\emph{Two characterizations of ellipsoidal cones}, J. Convex Analysis 20 (2013) 11811187]. Keywords: Ellipsoidal cone, ordered normed linear space, centrally symmetric convex body. MSC: 46B20; 52A50, 46B40, 46B10 [ Fulltextpdf (136 KB)] for subscribers only. 