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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0470857-2
PII: S 0002-9939(1975)0470857-2
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