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Zonoids whose polars are zonoids

Author: Rolf Schneider
Journal: Proc. Amer. Math. Soc. 50 (1975), 365-368
MSC: Primary 52A20
MathSciNet review: 0470857
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Abstract: It is shown that Euclidean $ n$-space contains nonellipsoidal, centrally symmetric convex bodies which, as well as their polars, are zonoids (i.e., can be approximated by finite sums of segments). This disproves a conjecture of E. D. Bolker.

References [Enhancements On Off] (What's this?)

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  • [4] R. Schneider, Zu einem Problem von Shephard über die Projektionen konvexer Körper, Math. Z. 101 (1967), 71-82. MR 36 #2059. MR 0218976 (36:2059)

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Keywords: Zonoid, range of vector measure, polar convex bodies, isometries of finite-dimensional subspaces of $ {L^1}$ and quotient spaces of $ {L^\infty }$
Article copyright: © Copyright 1975 American Mathematical Society

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