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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)


The dimension of almost spherical sections of convex bodies

Authors: T. Figiel, J. Lindenstrauss and V. D. Milman
Journal: Bull. Amer. Math. Soc. 82 (1976), 575-578
MSC (1970): Primary 52A20, 52A25, 46C05, 46E30
MathSciNet review: 0420223
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  • 1. Aryeh Dvoretzky, Some results on convex bodies and Banach spaces, Proc. Internat. Sympos. Linear Spaces (Jerusalem, 1960) Jerusalem Academic Press, Jerusalem; Pergamon, Oxford, 1961, pp. 123–160. MR 0139079 (25 #2518)
  • 2. Fritz John, Extremum problems with inequalities as subsidiary conditions, Studies and Essays Presented to R. Courant on his 60th Birthday, January 8, 1948, Interscience Publishers, Inc., New York, N. Y., 1948, pp. 187–204. MR 0030135 (10,719b)
  • 3. J. Lindenstrauss and L. Tzafriri, On the complemented subspaces problem, Israel J. Math. 9 (1971), 263–269. MR 0276734 (43 #2474)
  • 4. Bernard Maurey and Gilles Pisier, Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach, Studia Math. 58 (1976), no. 1, 45–90 (French). MR 0443015 (56 #1388)
  • 5. V. D. Milman, A new proof of A. Dvoretzky’s theorem on cross-sections of convex bodies, Funkcional. Anal. i Priložen. 5 (1971), no. 4, 28–37 (Russian). MR 0293374 (45 #2451)
  • 6. Erhard Schmidt, Die Brunn-Minkowskische Ungleichung und ihr Spiegelbild sowie die isoperimetrische Eigenschaft der Kugel in der euklidischen und nichteuklidischen Geometrie. I, Math. Nachr. 1 (1948), 81–157 (German). MR 0028600 (10,471d)

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PII: S 0002-9904(1976)14108-0