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Mat. Sb., 2019, Volume 210, Number 3, Pages 3–16 (Mi msb9012)  

Banach spaces with shortest network length depending only on pairwise distances between points

L. Sh. Burusheva

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

Abstract: For a real Banach space realising shortest networks for all finite subsets, we prove that a necessary and sufficient condition for the shortest network length to be expressed as a function only of pairwise distances between its points is that the space is either predual to $L_1$ or a Hilbert space. We give a characterization of spaces predual to $L_1$ and Hilbert spaces in terms of shortest networks.
Bibliography: 23 titles.

Keywords: Banach space, shortest network, Steiner point, Lindenstrauss spaces.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00333-а
Ministry of Education and Science of the Russian Federation НШ-6222.2018.1
Foundation for the Development of Theoretical Physics and Mathematics BASIS
This work was supported by the Russian Foundation for Basic Research (grant no. 18-01-00333-a), the Programme of the President of the Russian Federation for the support of leading scientific schools (grant no. НШ-6222.2018.1) and the BASIS Foundation for the Advancement of Theoretical Physics and Mathematics.


DOI: https://doi.org/10.4213/sm9012

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English version:
Sbornik: Mathematics, 2019, 210:3, 297–309

Bibliographic databases:

UDC: 517.982.256+515.124.4
MSC: 46B04, 46B20
Received: 22.09.2017 and 20.11.2018

Citation: L. Sh. Burusheva, “Banach spaces with shortest network length depending only on pairwise distances between points”, Mat. Sb., 210:3 (2019), 3–16; Sb. Math., 210:3 (2019), 297–309

Citation in format AMSBIB
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