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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 )

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 linéaireOrganisateurs de la rencontre : Albiac, Fernando ; Godefroy, Gilles ; Lancien, GillesDates : 05/03/2018 - 09/03/2018 Année de la rencontre : 2018 URL Congrès : https://conferences.cirm-math.fr/1755.htmlCitation 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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