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.
Supported by the Israel Science Foundation founded by the Academy of Sciences and Humanities.
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References
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
Milman V.D., Schechtman G. (1997) Global vs. local asymptotic theories of finite dimensional normed spaces. Duke J. 90:73–93
Talagrand M., Ledoux M. (1991) Probability in Banach spaces. A Series of Modern Surveys in Mathematics 23, 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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