Convex bodies with few faces

Authors:
Keith Ball and Alain Pajor

Journal:
Proc. Amer. Math. Soc. **110** (1990), 225-231

MSC:
Primary 52A40; Secondary 11H46, 52A20

DOI:
https://doi.org/10.1090/S0002-9939-1990-1019270-8

MathSciNet review:
1019270

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Abstract: It is proved that it are vectors in and

**[BF]**I. Bárány and Z. Füredi,*Computing the volume is difficult*, Discrete Comput. Geom.**2**(1987), 319-326. MR**911186 (89a:68203)****[BLM]**J. Bourgain, J. Lindenstrauss and V. D. Milman,*Approximation of zonoids by zonotopes*, Acta Math.**162**(1989), 73-141. MR**981200 (90g:46020)****[BP]**K. M. Ball and A. Pajor,*On the entropy of convex bodies with "few" extreme points*, in preparation.**[BV]**E. Bombieri and J. Vaaler,*On Stegel's lemma*, Invent. Math.**73**(1983), 11-32. MR**707346 (85g:11049a)****[CP]**B. Carl and A. Pajor,*Gelfand numbers of operators with values in a Hilbert space*, Invent. Math.**94**(1988), 479-504. MR**969241 (90d:46023)****[FJ]**T. Fiegiel and W. B. Johnson,*Large subspaces of**and estimates of the Gordon-Lewis constants*, Israel J. Math.**37**(1980), 92-112. MR**599305 (81m:46031)****[G]**E. D. Gluskin,*Extremal properties of rectangular parallelipipeds and their applications to the geometry of Banach spaces*, Mat. Sb. (N. S.)**136**(1988), 85-95.**[MeP]**M. Meyer and A. Pajor,*Sections of the unit ball of*, J. Funct. Anal.**80**(1988), 109-123. MR**960226 (89h:52010)****[MiP]**V. D. Milman and A. Pajor,*Isotropie position and inertia ellipsoids and zonoids of the unit ball of a normed**-dimensional space*, Israel seminar on G.A.F.A. (1987-88), Springer-Verlag, Lectures Notes in Math., vol. 1376, 1989. MR**1008717 (90g:52003)****[PT]**A. Pajor and N. Tomczak-Jaegermann,*Subspaces of small codimension of finite-dimensional Banach spaces*, Proc. Amer. Math. Soc.**97**(1986), 637-642. MR**845980 (87i:46040)****[S]**C. Schütt,*Entropy numbers of diagonal operators between symmetric Banach spaces*, J. Approx. Theory**40**(1984), 121-128. MR**732693 (85e:47029)****[V]**J. D. Vaaler,*A geometric inequality with applications to linear forms*, Pacific J. Math.**83**(1979), 543-553. MR**557952 (81d:52007)**

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DOI:
https://doi.org/10.1090/S0002-9939-1990-1019270-8

Article copyright:
© Copyright 1990
American Mathematical Society