Isometric embeddings of a class of separable metric spaces into Banach spaces
Sophocles K. Mercourakis; Vassiliadis G. Vassiliadis
Commentationes Mathematicae Universitatis Carolinae (2018)
- Volume: 59, Issue: 2, page 233-239
- ISSN: 0010-2628
Access Full Article
top
Abstract
topHow to cite
topMercourakis, Sophocles K., and Vassiliadis, Vassiliadis G.. "Isometric embeddings of a class of separable metric spaces into Banach spaces." Commentationes Mathematicae Universitatis Carolinae 59.2 (2018): 233-239. <http://eudml.org/doc/294810>.
@article{Mercourakis2018,
abstract = {Let $(M,d)$ be a bounded countable metric space and $c>0$ a constant, such that $d(x,y)+d(y,z)-d(x,z)\ge c$, for any pairwise distinct points $x,y,z$ of $M$. For such metric spaces we prove that they can be isometrically embedded into any Banach space containing an isomorphic copy of $\ell _\infty $.},
author = {Mercourakis, Sophocles K., Vassiliadis, Vassiliadis G.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {concave metric space; isometric embedding; separated set},
language = {eng},
number = {2},
pages = {233-239},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Isometric embeddings of a class of separable metric spaces into Banach spaces},
url = {http://eudml.org/doc/294810},
volume = {59},
year = {2018},
}
TY - JOUR
AU - Mercourakis, Sophocles K.
AU - Vassiliadis, Vassiliadis G.
TI - Isometric embeddings of a class of separable metric spaces into Banach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2018
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 59
IS - 2
SP - 233
EP - 239
AB - Let $(M,d)$ be a bounded countable metric space and $c>0$ a constant, such that $d(x,y)+d(y,z)-d(x,z)\ge c$, for any pairwise distinct points $x,y,z$ of $M$. For such metric spaces we prove that they can be isometrically embedded into any Banach space containing an isomorphic copy of $\ell _\infty $.
LA - eng
KW - concave metric space; isometric embedding; separated set
UR - http://eudml.org/doc/294810
ER -
References
top- Braß P., On equilateral simplices in normed spaces, Beiträge Algebra Geom. 40 (1999), no. 2, 303–307. MR1720106
- Elton J., Odell E., 10.4064/cm-44-1-105-109, Colloq. Math. 44 (1981), no. 1, 105–109. MR0633103DOI10.4064/cm-44-1-105-109
- Glakousakis E., Mercourakis S., 10.1112/S002557931400028X, Mathematika 61 (2015), no. 3, 547–558. MR3415641DOI10.1112/S002557931400028X
- Kilbane J., On embeddings of finite subsets of , available at arXiv:1609.08971v2 [math.FA] (2016), 12 pages. MR3767362
- Mercourakis S. K., Vassiliadis G., 10.1090/S0002-9939-2013-11746-6, Proc. Amer. Math. Soc. 142 (2014), no. 1, 205–212. MR3119196DOI10.1090/S0002-9939-2013-11746-6
- Ostrovskii M. I., Metric Embeddings. Bilipschitz and Coarse Embeddings into Banach Spaces, De Gruyter Studies in Mathematics, 49, De Gruyter, Berlin, 2013. MR3114782
- Partington J. R., 10.1112/blms/13.2.162, Bull. London Math. Soc. 13 (1981), no. 2, 162–166. MR0608103DOI10.1112/blms/13.2.162
- Swanepoel K. J., Equilateral sets in finite-dimensional normed spaces, Seminar of Mathematical Analysis, Colecc. Abierta, 71, Univ. Sevilla Secr. Publ., Seville, 2004, pp. 195–237. MR2117069
- Swanepoel K. J., Villa R., 10.1090/S0002-9939-07-08916-2, Proc. Amer. Math. Soc. 136 (2008), no. 1, 127–131. MR2350397DOI10.1090/S0002-9939-07-08916-2
- Swanepoel K. J., Villa R., 10.1007/s00454-013-9523-z, Discrete Comput. Geom. 50 (2013) no. 2, 354–373. MR3090523DOI10.1007/s00454-013-9523-z
- Talagrand M., 10.1007/BF02761372, Israel J. Math. 40 (1981) no. 3–4, 324–330 (French. English summary). MR0654587DOI10.1007/BF02761372
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.