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The Steiner Subratio in Banach Spaces

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Abstract

For every n = 2, 3,…, the minimum of the Steiner subratio is found for n-point sets in Banach spaces, and an example of a Banach space is constructed for which this minimum is attained. An example of a Banach space for which the minimum possible Steiner subratio equals 1/2 is also constructed.

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Acknowledgments

The author thanks P. A. Borodin for setting the problem, constant interest in the work, and valuable comments.

Funding

This work was supported by the Russian Foundation for Basic Research (grant 18-01-00333-a), by the program “Leading Scientific Schools” (grant NSh-6222.2018.1), and by the Development Fund “BASIS” for Theoretical Physics and Mathematics.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, 119991, Russia

    L. Sh. Burusheva

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  1. L. Sh. Burusheva
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Correspondence to L. Sh. Burusheva.

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Russian Text © The Author(s), 2019, published in Matematicheskie Zametki, 2019, Vol. 106, No. 2, pp. 188–197.

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Burusheva, L.S. The Steiner Subratio in Banach Spaces. Math Notes 106, 183–190 (2019). https://doi.org/10.1134/S0001434619070228

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  • DOI: https://doi.org/10.1134/S0001434619070228

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