English
On a difference between two methods of low-distortion embeddings of finite metric spaces into non-superreflexive Banach spaces
Multi angle
Auteurs : Randrianantoanina, Beata (Auteur de la Conférence)
CIRM (Editeur )
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
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 : 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
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
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 14/03/2018 Date de captation : 06/03/2018 Sous collection : Research talks arXiv category : Functional Analysis ; Metric Geometry Domaine : Analysis and its Applications ; Geometry Format : MP4 (.mp4) - HD Durée : 00:47:10 Audience : Researchers Download : https://videos.cirm-math.fr/2018-03-06_Randrianantoanina.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Non linear functional analysis / Analyse fonctionnelle non linéaireOrganisateurs 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
Données de citation
DOI : 10.24350/CIRM.V.19371703Citer cette vidéo: 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
- [ Post-edited] Coarse dimension reduction / Auteur de la Conférence Naor, Assaf.
- [Multi angle] $L^2$ spectral gap and group actions on Banach spaces / Auteur de la Conférence de la Salle, Mikael.
- [Multi angle] Finite quotients in coarse geometry / Auteur de la Conférence Khukhro, Anastasia.
- [Multi angle] Ideals in $L(L_p)$ / Auteur de la Conférence Johnson, William B..
Bibliographie
- Ostrovskii, M.I., & Randrianantoanina, B. (2017). A new approach to low-distortion embeddings of finite metric spaces into non-superreflexive Banach spaces.
