Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 24 (2017), No. 3, 795--805Copyright 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 [Abstract-pdf] 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 finite-dimensional cases proved by J. Jer{\'o}nimo-Castro and T. B. McAllister [\emph{Two characterizations of ellipsoidal cones}, J. Convex Analysis 20 (2013) 1181--1187]. Keywords: Ellipsoidal cone, ordered normed linear space, centrally symmetric convex body. MSC: 46B20; 52A50, 46B40, 46B10 [ Fulltext-pdf  (136  KB)] for subscribers only.