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Tytuł artykułu

Metric Characterizations of Superreflexivity in Terms of Word Hyperbolic Groups and Finite Graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We show that superreflexivity can be characterized in terms of bilipschitz embeddability of word hyperbolic groups.We compare characterizations of superrefiexivity in terms of diamond graphs and binary trees.We show that there exist sequences of series-parallel graphs of increasing topological complexitywhich admit uniformly bilipschitz embeddings into a Hilbert space, and thus do not characterize superrefiexivity.
Wydawca
Rocznik
Tom
2
Numer
1
Opis fizyczny
Daty
wydano
2014-01-01
otrzymano
2013-12-19
zaakceptowano
2014-04-22
online
2014-05-17
Twórcy
  • Department of Mathematics and Computer Science, St. John’s University, 8000 Utopia Parkway, Queens, NY 11439, USA, ostrovsm@stjohns.edu
Bibliografia
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  • [28] M. I. Ostrovskii, Embeddability of locally _nite metric spaces into Banach spaces is _nitely determined, Proc. Amer. Math. Soc., 140 (2012), 2721-2730. [29] M. I. Ostrovskii, Metric Embeddings: Bilipschitz and Coarse Embeddings into Banach Spaces, de Gruyter Studies in Mathematics, 49. Walter de Gruyter & Co., Berlin, 2013.
  • [30] M. I. Ostrovskii, Test-space characterizations of some classes of Banach spaces, in: Algebraic Methods in Functional Analysis, The Victor Shulman Anniversary Volume, I. G. Todorov, L. Turowska (Eds.), Operator Theory: Advances and Applications, Vol. 233, Birkhäuser, Basel, 2013, pp. 103-126.
  • [31] G. Pisier, Martingales in Banach spaces (in connection with type and cotype), Lecture notes of a course given at l’Institut Henri Poincaré, February 2-8, 2011, 242 pp; see the web site: http://perso-math.univ-mlv.fr/users/banach/Winterschool2011/
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  • [34] A. Sisto, Quasi-convexity of hyperbolically embedded subgroups, Math. Z. to appear, arXiv: 1310.7753.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_agms-2014-0005
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