Geodesic
Banach spaces with shortest network length depending only on pairwise distances between points
Sbornik. Mathematics, Tome 210 (2019) no. 3, pp. 297-309

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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
Mots-clés : Lindenstrauss spaces. 
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     author = {L. Sh. Burusheva},
     title = {Banach spaces with shortest network length depending only on pairwise distances between points},
     journal = {Sbornik. Mathematics},
     pages = {297--309},
     publisher = {mathdoc},
     volume = {210},
     number = {3},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2019_210_3_a0/}
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L. Sh. Burusheva. Banach spaces with shortest network length depending only on pairwise distances between points. Sbornik. Mathematics, Tome 210 (2019) no. 3, pp. 297-309. http://geodesic.mathdoc.fr/item/SM_2019_210_3_a0/