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Zap. Nauchn. Sem. POMI, 2008, Volume 360, Pages 153–161 (Mi znsl2163)  

This article is cited in 1 scientific paper (total in 1 paper)

On the coincidence of the canonical embeddings of a metric space into a Banach space

P. B. Zatitskii

Saint-Petersburg State University

Abstract: Recall the two classical canonical isometric embeddings of a finite metric space $X$ into a Banach space. That is, the Hausdorff–Kuratowsky embedding $x\to\rho(x,\cdot)$ into the space of continuous functions on $X$ with the max-norm, and the Kantorovich–Rubinshtein embedding $x\to\delta_x$ (where $\delta_x$ is the $\delta$-measure concentrated at $x$) with the transportation norm. We prove that these embeddings are not equivalent if $|X|>4$. Bibl. – 2 titles.

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English version:
Journal of Mathematical Sciences (New York), 2009, 158:6, 853–857

Bibliographic databases:

UDC: 515.124.4
Received: 17.11.2008

Citation: P. B. Zatitskii, “On the coincidence of the canonical embeddings of a metric space into a Banach space”, Representation theory, dynamics systems, combinatorial methods. Part XVI, Zap. Nauchn. Sem. POMI, 360, POMI, St. Petersburg, 2008, 153–161; J. Math. Sci. (N. Y.), 158:6 (2009), 853–857

Citation in format AMSBIB
\Bibitem{Zat08}
\by P.~B.~Zatitskii
\paper On the coincidence of the canonical embeddings of a~metric space into a~Banach space
\inbook Representation theory, dynamics systems, combinatorial methods. Part~XVI
\serial Zap. Nauchn. Sem. POMI
\yr 2008
\vol 360
\pages 153--161
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl2163}
\zmath{https://zbmath.org/?q=an:1188.46014}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2009
\vol 158
\issue 6
\pages 853--857
\crossref{https://doi.org/10.1007/s10958-009-9422-2}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-67349243418}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. P. B. Zatitskiy, “Canonical embeddings of compact metric spaces”, J. Math. Sci. (N. Y.), 174:1 (2011), 19–22  mathnet  crossref
  • Записки научных семинаров ПОМИ
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