Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl

PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2014 | 2 | 1 |

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

Bibliografia

  • [1] G. N. Arzhantseva, On quasiconvex subgroups of word hyperbolic groups, Geom. Dedicata, 87 (2001), no. 1-3, 191-208.
  • [2] F. Baudier, Metrical characterization of super-reflexivity and linear type of Banach spaces, Archiv Math., 89 (2007), no. 5, 419-429.[WoS]
  • [3] B. Beauzamy, Introduction to Banach spaces and their geometry. North-Holland Mathematics Studies, 68. Notas de Matemática [Mathematical Notes], 86. North-Holland Publishing Co., Amsterdam-New York, 1982. Second Edition: 1985.
  • [4] I. Benjamini, O. Schramm, Every graph with a positive Cheeger constant contains a tree with a positive Cheeger constant, Geom. Funct. Anal. 7 (1997), no. 3, 403-419.
  • [5] Y. Benyamini, J. Lindenstrauss, Geometric nonlinear functional analysis. Vol. 1. AmericanMathematical Society Colloquium Publications, 48. American Mathematical Society, Providence, RI, 2000.
  • [6] J. Bourgain, The metrical interpretation of superreflexivity in Banach spaces, Israel J. Math., 56 (1986), no. 2, 222-230.
  • [7] M. R. Bridson, A. Haefliger, Metric spaces of non-positive curvature. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 319. Springer-Verlag, Berlin, 1999.
  • [8] B. Brinkman, A. Karagiozova, J. R. Lee, Vertex cuts, random walks, and dimension reduction in series-parallel graphs, in: STOC’07-Proceedings of the 39th Annual ACM Symposium on Theory of Computing, 621-630, ACM, New York, 2007.
  • [9] S. Buyalo, A. Dranishnikov, V. Schroeder, Embedding of hyperbolic groups into products of binary trees, Invent. Math., 169 (2007), no. 1, 153-192.
  • [10] S. Buyalo, V. Schroeder, Elements of asymptotic geometry, EMS Monographs in Mathematics, European Mathematical Society (EMS), Zürich, 2007.
  • [11] F. Dahmani, V. Guirardel, D. Osin, Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces, arXiv:1111.7048v3.
  • [12] R. Deville, G. Godefroy, V. Zizler, Smoothness and renormings in Banach spaces, Pitman Monographs and Surveys in Pure and Applied Mathematics, 64, Longman Scienti_c & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1993.
  • [13] M. Deza, M. Laurent, Geometry of cuts and metrics. Algorithms and Combinatorics, 15. Springer-Verlag, Berlin, 1997.
  • [14] D. van Dulst, Reflexive and superreflexive Banach spaces. Mathematical Centre Tracts, 102. Mathematisch Centrum, Amsterdam, 1978.
  • [15] J. Elton, E. Odell, The unit ball of every in_nite-dimensional normed linear space contains a (1 + ")-separated sequence. Colloq. Math. 44 (1981), no. 1, 105-109.
  • [16] P. Enflo, Banach spaces which can be given an equivalent uniformly convex norm, Israel J. Math, 13 (1972), 281-288.
  • [17] D. Eppstein, Parallel recognition of series-parallel graphs. Inform. and Comput. 98 (1992), no. 1, 41-55.
  • [18] M. Gromov, Hyperbolic groups, in: Essays in group theory, 75-263,Math. Sci. Res. Inst. Publ., 8, Springer, New York, 1987.; Russian translation: Institute of Computer Science, Izhevsk, 2002.
  • [19] A. Gupta, I. Newman, Y. Rabinovich, A. Sinclair, Cuts, trees and `1-embeddings of graphs, Combinatorica, 24 (2004) 233-269; Conference version in: 40th Annual IEEE Symposium on Foundations of Computer Science, 1999, pp. 399-408.
  • [20] R. C. James, Uniformly non-square Banach spaces. Ann. of Math. (2) 80 (1964), 542-550.
  • [21] R. C. James, Some self-dual properties of normed linear spaces, in: Symposiumon In_nite-Dimensional Topology (Louisiana State Univ., Baton Rouge, La., 1967), pp. 159-175. Ann. ofMath. Studies, No. 69, Princeton Univ. Press, Princeton, N. J., 1972.
  • [22] R. C. James, Super-reflexive Banach spaces, Canad. J. Math., 24 (1972), 896-904.
  • [23] W. B. Johnson, G. Schechtman, Diamond graphs and super-reflexivity, J. Topol. Anal., 1 (2009), no. 2, 177-189.[WoS][Crossref]
  • [24] B. Kloeckner, Yet another short proof of the Bourgain’s distortion estimate for embedding of trees into uniformly convex Banach spaces, Israel J. Math., to appear, DOI: 10.1007/s11856-014-0024-4, http://www-fourier.ujfgrenoble.fr/_bkloeckn/recherche.html[Crossref]
  • [25] C. A. Kottman, Subsets of the unit ball that are separated by more than one. Studia Math. 53 (1975), no. 1, 15-27.
  • [26] M. Mendel, A. Naor, Markov convexity and local rigidity of distorted metrics, J. Eur. Math. Soc. (JEMS), 15 (2013), no. 1, 287-337; Conference version: Computational geometry (SCG’08), 49-58, ACM, New York, 2008.[Crossref]
  • [27] P.W. Nowak, G. Yu, Large scale geometry. EMS Textbooks in Mathematics. European Mathematical Society (EMS), Zürich, 2012.
  • [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/
  • [32] Y. Rabinovich, R. Raz, Lower bounds on the distortion of embedding _nite metric spaces in graphs, Discrete Comput. Geom., 19 (1998), no. 1, 79-94.
  • [33] J. J. Schä_er, K. Sundaresan, Reflexivity and the girth of spheres. Math. Ann. 184 (1969/1970) 163-168.
  • [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
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.