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Remarks on minkowski symmetrizations

Part of the Lecture Notes in Mathematics book series (LNM,volume 1745)

Abstract

Here we extend a result by J. Bourgain, J. Lindenstrauss, V.D. Milman on the number of random Minkowski symmetrizations needed to obtain an approximated ball, if we start from an arbitrary convex body in ℝn. We also show that the number of “deterministic” symmetrizations needed to approximate an Euclidean ball may be significantly smaller than the number of “random” ones.

Keywords

  • Convex Hull
  • Convex Body
  • Numerical Constant
  • Euclidean Ball
  • Dual Norm

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Supported by the Israel Science Foundation founded by the Academy of Sciences and Humanities.

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References

  1. Bourgain J., Lindenstrauss J., Milman V.D. (1988) Minkowski sums and symmetrizations. In: Lindenstrauss J., Milman V.D. (Eds.) Geometric Aspects of Functional Analysis (1986–87), Lecture Notes in Math., 1317, Springer-Verlag, 44–66

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  2. Milman V.D., Schechtman G. (1997) Global vs. local asymptotic theories of finite dimensional normed spaces. Duke J. 90:73–93

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  3. Talagrand M., Ledoux M. (1991) Probability in Banach spaces. A Series of Modern Surveys in Mathematics 23, Springer-Verlag

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© 2000 Springer-Verlag

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Klartag, B. (2000). Remarks on minkowski symmetrizations. In: Milman, V.D., Schechtman, G. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 1745. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0107211

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  • DOI: https://doi.org/10.1007/BFb0107211

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41070-6

  • Online ISBN: 978-3-540-45392-5

  • eBook Packages: Springer Book Archive