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The distance between certainn-dimensional Banach spaces

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Abstract

IfE andF aren-dimensional Banach spaces, ifE has cotype 2, and if the ball ofF* has a small number of extreme points, then the Banach-Mazur distanced(E, F)≦C √nlogn. The techniques lead to the formally stronger result: IfE andF* have type 2 constantsa andb, respectively, thend(E, F)≦√n(a+b). IfE isn-dimensional, the identity map onE, when restricted to a large subspace ofE, factors through\(l_\infty ^n \) with normC √n.

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Authors and Affiliations

  1. Ohio State University, 43210, Columbus, Ohio, USA

    W. J. Davis, V. D. Milman & N. Tomczak-Jaegermann

  2. Wayne State University, Detroit, Michigan, USA

    W. J. Davis, V. D. Milman & N. Tomczak-Jaegermann

  3. Tel Aviv University, Ramat Aviv, Israel

    W. J. Davis, V. D. Milman & N. Tomczak-Jaegermann

  4. Ohio State University, 43210, Columbus, Ohio, USA

    W. J. Davis, V. D. Milman & N. Tomczak-Jaegermann

  5. University of Warsaw, Warsaw, Poland

    W. J. Davis, V. D. Milman & N. Tomczak-Jaegermann

Authors
  1. W. J. Davis
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  2. V. D. Milman
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  3. N. Tomczak-Jaegermann
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Additional information

The authors’ work was supported in part, respectively, by NSF grant numbers MCS 78-02194, MCS 79-02489, and MCS 77-04174.

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Davis, W.J., Milman, V.D. & Tomczak-Jaegermann, N. The distance between certainn-dimensional Banach spaces. Israel J. Math. 39, 1–15 (1981). https://doi.org/10.1007/BF02762849

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  • DOI: https://doi.org/10.1007/BF02762849

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