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H 1 On a difference between two methods of low-distortion embeddings of finite metric spaces into non-superreflexive Banach spaces

Auteurs : Randrianantoanina, Beata (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : In a recent paper, the speaker and M.I. Ostrovskii developed a new metric embedding method based on the theory of equal-signs-additive (ESA) sequences developed by Brunel and Sucheston in 1970’s. This method was used to construct bilipschitz embeddings of diamond and Laakso graphs with an arbitrary finite number of branches into any non-superreflexive Banach space with a uniform bound on distortions that is independent of the number of branches.
    In this talk we will outline a proof that the above mentioned embeddability results cannot be obtained using the embedding method which was used for trees by Bourgain (1986) and for binary branching diamonds and Laakso graphs by Johnson and Schechtman (2009), and which is based on a classical James’ characterization of superreflexivity (the factorization between the summing basis and the unit vector basis of $\ell_1$). Our proof uses a “self-improvement” argument and the Ramsey theorem.
    Joint work with M.I. Ostrovskii.

    Keywords : diamond graph; equal-signs-additive sequence; metric characterization; superreflexive Banach space

    Codes MSC :
    05C12 - Distance in graphs
    46B07 - Local theory of Banach spaces
    46B10 - Duality and reflexivity
    46B85 - Embeddings of discrete metric spaces into Banach spaces; applications
    30L05 - Geometric embeddings of metric spaces

    Ressources complémentaires :
    https://www.cirm-math.fr/ProgWeebly/Renc1755/Randrianantoanina.pdf

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 14/03/2018
      Date de captation : 06/03/2018
      Collection : Research talks ; Analysis and its Applications ; Geometry
      Format : MP4
      Durée : 00:47:10
      Domaine : Analysis and its Applications ; Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2018-03-06_Randrianantoanina.mp4

    Informations sur la rencontre

    Nom de la rencontre : Non linear functional analysis / Analyse fonctionnelle non linéaire
    Organisateurs de la rencontre : Albiac, Fernando ; Godefroy, Gilles ; Lancien, Gilles
    Dates : 05/03/2018 - 09/03/2018
    Année de la rencontre : 2018
    URL Congrès : https://conferences.cirm-math.fr/1755.html

    Citation Data

    DOI : 10.24350/CIRM.V.19371703
    Cite this video as: Randrianantoanina, Beata (2018). On a difference between two methods of low-distortion embeddings of finite metric spaces into non-superreflexive Banach spaces. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19371703
    URI : http://dx.doi.org/10.24350/CIRM.V.19371703


    Voir aussi

    Bibliographie

    1. Ostrovskii, M.I., & Randrianantoanina, B. (2017). A new approach to low-distortion embeddings of finite metric spaces into non-superreflexive Banach spaces. - https://arxiv.org/abs/1609.06618

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