×

zbMATH — the first resource for mathematics

The dimension of almost spherical sections of convex bodies. (English) Zbl 0375.52002

MSC:
52A05 Convex sets without dimension restrictions (aspects of convex geometry)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Barnette, D., The minimum number of vertices of a simple polytope.Israel J. Math., 10 (1971), 121–125. · Zbl 0221.52004
[2] Bennett, G., Dor, L. E., Goodman, V., Johnson, W. B. &Newman, C. M., On uncomplemented subspaces ofL p , 1<p<2.Israel J. Math., 26 (1977), 178–187. · Zbl 0339.46022
[3] Davis, W. J., Dean, D. W. &Singer, I., Complemented subspaces and A systems in Banach spaces,Israel J. Math., 6 (1968), 303–309. · Zbl 0169.15401
[4] Day, M. M.,Normed linear spaces, Springer Verlag 1973.
[5] Dinghas, A., Einfacher beweis der isoperimetrischen Eigenschaft der Kugel in Riemannschen Räumen konstanter Krümmung.Math. Nachr., 2 (1949), 148–162. · Zbl 0032.31203
[6] Dvoretzky, A., Some results on convex bodies and Banach spaces.Proc. Int. Symp. on linear spaces, Jerusalem 1961, 123–160. · Zbl 0119.31803
[7] Dvoretzky, A. &Rogers, C. A., Absolute and unconditional convergence in normed linear spaces.Proc. Nat. Acad. Sci. U.S.A., 36 (1950), 192–197. · Zbl 0036.36303
[8] Enflo, P., Lindenstrauss, J. &Pisier, G., On the three space problem.Math. Scand., 36 (1975), 199–210. · Zbl 0314.46015
[9] Figiel, T., A short proof of Dvoretzky’s theorme on almost spherical sections.Compositio Math., 33 (1976), 297–301. · Zbl 0343.52004
[10] Figiel, T., Lindenstrauss, J. &Milman V. D., The dimension of almost spherical sections of convex bodies.Bull. Amer. Math. Soc., 82 (1976), 575–578. · Zbl 0329.52003
[11] Figiel, T. &Pisier, G., Séries aléatoires dans les espaces uniformément convexes ou uniformément lisses.C. R. Acad. Sci. Paris, 279 (1974), 611–614. · Zbl 0326.46007
[12] Garling, D. J. H. &Gordon, Y., Relations between some constants associated with finite-dimensional Banach spaces.Israel J. Math., 9 (1971), 346–361. · Zbl 0212.14203
[13] Grothendieck, A., Resumé de la theorie metrique des produits tensoriels topologique.Bol. Soc. Matem. São Paulo, 8 (1956), 1–79.
[14] Hadwiger, H.,Vorlesung über Inhalt, Oberfläche und Isoperimetric. Springer Verlag 1957. · Zbl 0078.35703
[15] John, F. Extremum problems with inequalities as subsidiary conditions. Courant anniversary volume. Interscience, New York 1948, 187–204.
[16] Johnson, W. B., A reflexive Banach space which is not sufficiently Euclidean.Studia Math., 55 (1976), 201–205. · Zbl 0362.46015
[17] Kadec, M. I. &Snobar, M. G., Certain functionals on the Minkowsky compactum.Mat. Zametki, 10 (1971), 694–696 (translated from Russian).
[18] Kahane, J. P.,Some random series of functions. Health Mathematical Monographs 1968. · Zbl 0192.53801
[19] Krivine, J. L., Sous-espaces de dimension fini des espaces de Banach reticulés.Ann. of Math., 104 (1976), 1–29. · Zbl 0329.46008
[20] Kwapien, S., Isomorphic characterization of inner product spaces by orthogonal series with vector valued coefficients.Studia Math., 44 (1972), 583–595. · Zbl 0256.46024
[21] Larman, D. G. &Mani, P., Almost ellipsoidal sections and projections of convex bodies.Proc. Cambridge Philos. Soc. 77 (1975), 529–546. · Zbl 0318.52006
[22] Levy, P.,Problèmes concrets d’analyse functionelle, Gauthier Villars Paris 1951.
[23] Lindenstrauss, J. &Pelczynski, A., Absolutely summing operators in £ p spaces and their applications.Studia Math., 29 (1968), 275–326. · Zbl 0183.40501
[24] Lindenstrauss, J. &Tzafriri, L., On the complemented subspaces problem.Israel J. Math., 9 (1971), 263–269. · Zbl 0211.16301
[25] Maleev, R. P. &Troyanski, S. L., On the moduli of convexity and smoothness of Orlicz spaces.Studia Math., 54 (1975), 131–141. · Zbl 0328.46025
[26] Maurey, B., Un théorème de prolongement.C. R. Acad. Sci. Paris., Sér A-B, 279 (1974), 329–332. · Zbl 0291.47001
[27] 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. · Zbl 0269.46015
[28] Maurey, B. &Pisier, G., Series de variables aléatoires vectorielles independantes et propriétés geometriques des espaces de Banach.Studia Math. 58 (1976), 45–90. · Zbl 0344.47014
[29] 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).
[30] Pelczynski, A. &Rosenthal, H. P., Localization techniques inL p spaces.Studia Math., 52 (1975), 263–289.
[31] Rutovitz, D., Some parameters associated with finite-dimensional Banach spaces.J. London Math. Soc., 40 (1965), 241–255. · Zbl 0125.06402
[32] Szankowski, A., On Dvoretzky’s theorem on almost spherical sections of convex bodies.Israel J. Math., 17 (1974), 325–338. · Zbl 0288.52002
[33] Schmidt, E., Die Brunn-Minkowski ungleichung.Math. Nachr., 1 (1948), 81–157. · Zbl 0030.07602
[34] Tomczak-Jaegermann, E., The moduli of smoothness and convexity and the Rademacher averages of trace classesS p , 1<Studia Math., 50 (1974), 163–182. · Zbl 0282.46016
[35] Tzafriri, L., On Banach spaces with unconditional bases.Israel J. Math., 17 (1974), 84–93. · Zbl 0281.46013
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.