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Tytuł artykułu

Tight Embeddability of Proper and Stable Metric Spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We introduce the notions of almost Lipschitz embeddability and nearly isometric embeddability. We prove that for p ∈ [1,∞], every proper subset of Lp is almost Lipschitzly embeddable into a Banach space X if and only if X contains uniformly the ℓpn’s. We also sharpen a result of N. Kalton by showing that every stable metric space is nearly isometrically embeddable in the class of reflexive Banach spaces.
Wydawca
Rocznik
Tom
3
Numer
1
Opis fizyczny
Daty
otrzymano
2015-03-20
zaakceptowano
2015-05-27
online
2015-07-01
Twórcy
autor
  • Institut de Mathématiques Jussieu-Paris Rive Gauche, Université Pierre et Marie Curie, Paris, France and Department of Mathematics, Texas A&M University, College Station, TX 77843, USA
autor
  • Laboratoire de Mathématiques de Besançon, Université de Franche-Comté, 16 route de Gray, 25030 Besançon Cédex, France
Bibliografia
  • [1] Y. Bartal and L. Gottlieb. Dimension reduction techniques for ℓp, 1 ℓ p < ∞, with applications. arXiv:1408.1789, 2014.
  • [2] F. Baudier. Quantitative nonlinear embeddings into Lebesgue sequence spaces. J. Topol. Anal., to appear, arXiv: 1210.0588 (2013), 32 pages.
  • [3] F. Baudier. Metrical characterization of super-reflexivity and linear type of Banach spaces. Arch. Math., 89:419–429, 2007. [WoS][Crossref]
  • [4] F. Baudier. Plongements des espaces métriques dans les espaces de Banach. Ph.D. Thesis, 100 pages (French), 2009.
  • [5] F. Baudier. Embeddings of proper metric spaces into Banach spaces. Hous. J. Math., 38:209–223, 2012.
  • [6] F. Baudier and G. Lancien. Embeddings of locally finite metric spaces into Banach spaces. Proc. Amer. Math. Soc., 136: 1029–1033, 2008.
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  • [10] D. J. H. Garling. Stable Banach spaces, random measures and Orlicz function spaces. In Probability measures on groups (Oberwolfach, 1981), volume 928 of Lecture Notes in Math., pages 121–175. Springer, Berlin-New York, 1982.
  • [11] G. Godefroy and N. J. Kalton. Lipschitz-free Banach spaces. Studia Math., 159:121–141, 2003.
  • [12] M. Gromov. Asymptotic invariants of infinite groups, Geometric group theory, Vol. 2 (Sussex, 1991), London Math. Soc. Lecture Note Ser., vol. 182, Cambridge Univ. Press, Cambridge, 1993, pp. 1–295.
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  • [15] R. C. James. Uniformly non-square Banach spaces. Ann. of Math. (2), 80:542–550, 1964.
  • [16] W. B. Johnson and J. Lindenstrauss, editors. Handbook of the geometry of Banach spaces. Vol. I. North-Holland Publishing Co., Amsterdam, 2001.
  • [17] N. J. Kalton. Coarse and uniform embeddings into reflexive spaces. Quart. J. Math. (Oxford), 58:393–414, 2007. [WoS]
  • [18] N. J. Kalton and N. L. Randrianarivony. The coarse Lipschitz structure of `p `q. Math. Ann., 341:223–237, 2008.
  • [19] J. L. Krivine. Sous-espaces de dimension finie des espaces de Banach réticulés. Ann. of Math. (2), 104:1–29, 1976.
  • [20] J. L. Krivine and B. Maurey. Espaces de Banach stables. Israel J. Math., 39:273–295, 1981.
  • [21] Å. Lima, O. Nygaard, and E. Oja. Isometric factorization of weakly compact operators and the approximation property. Israel J. Math., 119:325–348, 2000.
  • [22] Y. Lindenstrauss and L. Tzafriri. Classical Banach Spaces, volume 338 of Lecture Notes Math. Springer-Verlag, 1979.
  • [23] A. I. Markushevich. On a basis in a wide sense for linear spaces. Dokl. Akad. Nauk., 41:241–244, 1943.
  • [24] B.Maurey and G. Pisier. Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach. Studia Math., 58:45–90, 1976.
  • [25] P. Nowak and G. Yu. Large scale geometry. EMS Textbooks in Mathematics. European Mathematical Society (EMS), Zürich, 2012.
  • [26] M. I. Ostrovskii. Embeddability of locally finite metric spaces into Banach spaces is finitely determined. Proc. Amer. Math. Soc., 140(8):2721–2730, 2012.
  • [27] R. Ostrovsky and Y. Rabani. Polynomial-time approximation schemes for geometric min-sum median clustering. J. ACM, 49 (2):139–156 (electronic), 2002. [Crossref]
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_agms-2015-0010
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