Duke Mathematical Journal

Global versus local asymptotic theories of finite-dimensional normed spaces

V. D. Milman and G. Schechtman

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Article information

Source
Duke Math. J., Volume 90, Number 1 (1997), 73-93.

Dates
First available in Project Euclid: 19 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077232448

Digital Object Identifier
doi:10.1215/S0012-7094-97-09003-7

Mathematical Reviews number (MathSciNet)
MR1478544

Zentralblatt MATH identifier
0911.52002

Subjects
Primary: 46B07: Local theory of Banach spaces
Secondary: 52A20: Convex sets in n dimensions (including convex hypersurfaces) [See also 53A07, 53C45]

Citation

Milman, V. D.; Schechtman, G. Global versus local asymptotic theories of finite-dimensional normed spaces. Duke Math. J. 90 (1997), no. 1, 73--93. doi:10.1215/S0012-7094-97-09003-7. https://projecteuclid.org/euclid.dmj/1077232448


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References

  • [B] K. Ball, The plank problem for symmetric bodies, Invent. Math. 104 (1991), no. 3, 535–543.
  • [Ba] T. Bang, A solution of the “plank problem.”, Proc. Amer. Math. Soc. 2 (1951), 990–993.
  • [BLM] J. Bourgain, J. Lindenstrauss, and V. D. Milman, Minkowski sums and symmetrizations, Geometric aspects of functional analysis (Israel Seminar, 1986–87), Lecture Notes in Math., vol. 1317, Springer, Berlin, 1988, pp. 44–66.
  • [BM1] J. Bourgain and V. D. Milman, New volume ratio properties for convex symmetric bodies in $\bf R\sp n$, Invent. Math. 88 (1987), no. 2, 319–340.
  • [BM2] J. Bourgain and V. D. Milman, Sections euclidiennes et volume des corps symétriques convexes dans $\bf R\sp n$, C. R. Acad. Sci. Paris Sér. I Math. 300 (1985), no. 13, 435–438.
  • [FLM] T. Figiel, J. Lindenstrauss, and V. D. Milman, The dimension of almost spherical sections of convex bodies, Acta Math. 139 (1977), no. 1-2, 53–94.
  • [G] Y. Gordon, Some inequalities for Gaussian processes and applications, Israel J. Math. 50 (1985), no. 4, 265–289.
  • [Ka] B. S. Kašin, Orders of the widths of certain classes of smooth functions, Uspehi Mat. Nauk 32 (1977), no. 1(193), 191–192.
  • [Mi1] 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.
  • [Mi2] V. D. Milman, Inégalité de Brunn-Minkowski inverse et applications à la théorie locale des espaces normés, C. R. Acad. Sci. Paris Sér. I Math. 302 (1986), no. 1, 25–28.
  • [Mi3] V. D. Milman, Spectrum of a position of a convex body and linear duality relations, Festschrift in honor of I. I. Piatetski-Shapiro on the occasion of his sixtieth birthday, Part II (Ramat Aviv, 1989), Israel Math. Conf. Proc., vol. 3, Weizmann, Jerusalem, 1990, pp. 151–161.
  • [Mi4] V. D. Milman, Some applications of duality relations, Geometric aspects of functional analysis (1989–90), Lecture Notes in Math., vol. 1469, Springer, Berlin, 1991, pp. 13–40.
  • [MS] V. D. Milman and G. Schechtman, Asymptotic theory of finite-dimensional normed spaces, Lecture Notes in Mathematics, vol. 1200, Springer-Verlag, Berlin, 1986.
  • [Pi] G. Pisier, The volume of convex bodies and Banach space geometry, Cambridge Tracts in Mathematics, vol. 94, Cambridge University Press, Cambridge, 1989.
  • [Sc] G. Schechtman, A remark concerning the dependence on $\epsilon$ in Dvoretzky's theorem, Geometric aspects of functional analysis (1987–88), Lecture Notes in Math., vol. 1376, Springer, Berlin, 1989, pp. 274–277.
  • [Schm] M. Schmuckenschläger, On the dependence on $\epsilon$ in a theorem of J. Bourgain, J. Lindenstrauss and V. D. Milman, Geometric aspects of functional analysis (Israel Seminar, 1989–90), Lecture Notes in Math., vol. 1469, Springer, Berlin, 1991, pp. 166–173.
  • [ST] S. Szarek and N. Tomczak-Jaegermann, On nearly Euclidean decomposition for some classes of Banach spaces, Compositio Math. 40 (1980), no. 3, 367–385.
  • [To] N. Tomczak-Jaegermann, Banach-Mazur distances and finite-dimensional operator ideals, Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 38, Longman Scientific & Technical, Harlow, 1989.