Acta Mathematica

The dimension of almost spherical sections of convex bodies

T. Figiel, J. Lindenstrauss, and V. D. Milman

Full-text: Open access

Note

Research supported in part by NSF Grant MPS 74-07509-A02.

Article information

Source
Acta Math. Volume 139 (1977), 53-94.

Dates
Received: 23 August 1976
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485889965

Digital Object Identifier
doi:10.1007/BF02392234

Zentralblatt MATH identifier
0375.52002

Rights
1977 © Almqvist & Wiksell

Citation

Figiel, T.; Lindenstrauss, J.; Milman, V. D. The dimension of almost spherical sections of convex bodies. Acta Math. 139 (1977), 53--94. doi:10.1007/BF02392234. https://projecteuclid.org/euclid.acta/1485889965


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References

  • Barnette, D., The minimum number of vertices of a simple polytope. Israel J. Math., 10 (1971), 121–125.
  • Bennett, G., Dor, L. E., Goodman, V., Johnson, W. B. & Newman, C. M., On uncomplemented subspaces of Lp, 1< p<2. Israel J. Math., 26 (1977), 178–187.
  • Davis, W. J., Dean, D. W. & Singer, I., Complemented subspaces and A systems in Banach spaces, Israel J. Math., 6 (1968), 303–309.
  • Day, M. M., Normed linear spaces, Springer Verlag 1973.
  • Dinghas, A., Einfacher beweis der isoperimetrischen Eigenschaft der Kugel in Riemannschen Räumen konstanter Krümmung. Math. Nachr., 2 (1949), 148–162.
  • Dvoretzky, A., Some results on convex bodies and Banach spaces. Proc. Int. Symp. on linear spaces, Jerusalem 1961, 123–160.
  • Dvoretzky, A. & Rogers, C. A., Absolute and unconditional convergence in normed linear spaces. Proc. Nat. Acad. Sci. U.S.A., 36 (1950), 192–197.
  • Enflo, P., Lindenstrauss, J. & Pisier, G., On the three space problem. Math. Scand., 36 (1975), 199–210.
  • Figiel, T., A short proof of Dvoretzky's theorme on almost spherical sections. Compositio Math., 33 (1976), 297–301.
  • Figiel, T., Lindenstrauss, J. & Milman V. D., The dimension of almost spherical sections of convex bodies. Bull. Amer. Math. Soc., 82 (1976), 575–578.
  • Figiel, T. & Pisier, G., Séries aléatoires dans les espaces uniformément convexes ou uniformément lisses. C. R. Acad. Sci. Paris, 279 (1974), 611–614.
  • Garling, D. J. H. & Gordon, Y., Relations between some constants associated with finite-dimensional Banach spaces. Israel J. Math., 9 (1971), 346–361.
  • Grothendieck, A., Resumé de la theorie metrique des produits tensoriels topologique. Bol. Soc. Matem. São Paulo, 8 (1956), 1–79.
  • Hadwiger, H., Vorlesung über Inhalt, Oberfläche und Isoperimetric. Springer Verlag 1957.
  • John, F.Extremum problems with inequalities as subsidiary conditions. Courant anniversary volume. Interscience, New York 1948, 187–204.
  • Johnson, W. B., A reflexive Banach space which is not sufficiently Euclidean. Studia Math., 55 (1976), 201–205.
  • Kadec, M. I. & Snobar, M. G., Certain functionals on the Minkowsky compactum. Mat. Zametki, 10 (1971), 694–696 (translated from Russian).
  • Kahane, J. P., Some random series of functions. Health Mathematical Monographs 1968.
  • Krivine, J. L., Sous-espaces de dimension fini des espaces de Banach reticulés. Ann. of Math., 104 (1976), 1–29.
  • Kwapien, S., Isomorphic characterization of inner product spaces by orthogonal series with vector valued coefficients. Studia Math., 44 (1972), 583–595.
  • Larman, D. G. & Mani, P., Almost ellipsoidal sections and projections of convex bodies. Proc. Cambridge Philos. Soc. 77 (1975), 529–546.
  • Levy, P., Problèmes concrets d'analyse functionelle, Gauthier Villars Paris 1951.
  • Lindenstrauss, J. & Pelczynski, A., Absolutely summing operators in £p spaces and their applications. Studia Math., 29 (1968), 275–326.
  • Lindenstrauss, J. & Tzafriri, L., On the complemented subspaces problem. Israel J. Math., 9 (1971), 263–269.
  • Maleev, R. P. & Troyanski, S. L., On the moduli of convexity and smoothness of Orlicz spaces. Studia Math., 54 (1975), 131–141.
  • Maurey, B., Un théorème de prolongement. C. R. Acad. Sci. Paris., Sér A-B, 279 (1974), 329–332.
  • Maurey, B. & Pisier, G., Caractérisation d'une classe d'espaces de Banach par de propriétés des series aléatoires vectorielles. C. R. Acad. Sci. Paris, 277 (1973), 687–690.
  • Maurey, B. & Pisier, G., Series de variables aléatoires vectorielles independantes et propriétés geometriques des espaces de Banach. Studia Math. 58 (1976), 45–90.
  • Milman, V. D., A new proof of the theorem of A. Dvoretzky on sections of convex bodies. Funct. Anal. Appl. 5 (1971), 28–37 (translated from Russian).
  • Pelczynski, A. & Rosenthal, H. P., Localization techniques in Lp spaces. Studia Math., 52 (1975), 263–289.
  • Rutovitz, D., Some parameters associated with finite-dimensional Banach spaces. J. London Math. Soc., 40 (1965), 241–255.
  • Szankowski, A., On Dvoretzky's theorem on almost spherical sections of convex bodies. Israel J. Math., 17 (1974), 325–338.
  • Schmidt, E., Die Brunn-Minkowski ungleichung. Math. Nachr., 1 (1948), 81–157.
  • Tomczak-Jaegermann, E., The moduli of smoothness and convexity and the Rademacher averages of trace classes Sp, 1≤p<∞. Studia Math., 50 (1974), 163–182.
  • Tzafriri, L., On Banach spaces with unconditional bases. Israel J. Math., 17 (1974), 84–93.