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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb., 2014 Volume 205, Number 4, Pages 3–20 (Mi sm8264)

This article is cited in 14 papers

Banach spaces that realize minimal fillings

B. B. Bednov, P. A. Borodin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: It is proved that a real Banach space realizes minimal fillings for all its finite subsets (a shortest network spanning a fixed finite subset always exists and has the minimum possible length) if and only if it is a predual of $L_1$. The spaces $L_1$ are characterized in terms of Steiner points (medians).
Bibliography: 25 titles.

Keywords: Banach space, shortest network, minimal filling, Steiner point (median).

UDC: 517.982.256+515.124.4

MSC: Primary 46B04; Secondary 05C12, 54E35

Received: 19.06.2013 and 06.11.2013

DOI: 10.4213/sm8264


 English version:
Sbornik: Mathematics, 2014, 205:4, 459–475

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