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Sbornik: Mathematics, 2014, Volume 205, Issue 4, Pages 459–475
DOI: https://doi.org/10.1070/SM2014v205n04ABEH004383 (Mi sm8264) 		 
This article is cited in 14 scientific papers (total 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
English version PDF (491 kB) Citations (14) Russian version article
References:
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DOI: https://doi.org/10.1070/SM2014v205n04ABEH004383
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).
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00510
14-01-91158
Ministry of Education and Science of the Russian Federation НШ-3682.2014.1
Received: 19.06.2013 and 06.11.2013
Bibliographic databases:
Document Type: Article
UDC: 517.982.256+515.124.4
MSC: Primary 46B04; Secondary 05C12, 54E35
Language: English
Original paper language: Russian
Citation: B. B. Bednov, P. A. Borodin, “Banach spaces that realize minimal fillings”, Sb. Math., 205:4 (2014), 459–475
Citation in format AMSBIB
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник Sbornik: Mathematics
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    Abstract page:924
    Russian version PDF:344
    English version PDF:28
    References:106
    First page:82
     
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