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On a difference between two methods of low-distortion embeddings of finite metric spaces into non-superreflexive Banach spaces
Multi angle
Authors : Randrianantoanina, Beata (Author of the conference)
CIRM (Publisher )
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
Additional resources :
https://www.cirm-math.fr/ProgWeebly/Renc1755/Randrianantoanina.pdf
CIRM (Publisher )
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Abstract :
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
MSC Codes : 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
Additional resources :
https://www.cirm-math.fr/ProgWeebly/Renc1755/Randrianantoanina.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 14/03/2018 Conference Date : 06/03/2018 Subseries : Research talks arXiv category : Functional Analysis ; Metric Geometry Mathematical Area(s) : Analysis and its Applications ; Geometry Format : MP4 (.mp4) - HD Video Time : 00:47:10 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2018-03-06_Randrianantoanina.mp4 
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Information on the Event
Event Title : Non linear functional analysis / Analyse fonctionnelle non linéaireEvent Organizers : Albiac, Fernando ; Godefroy, Gilles ; Lancien, Gilles Dates : 05/03/2018 - 09/03/2018 Event Year : 2018 Event URL : https://conferences.cirm-math.fr/1755.html
Citation Data
DOI : 10.24350/CIRM.V.19371703Cite 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 |
See Also
- [Post-edited] Coarse dimension reduction / Author of the conference Naor, Assaf.
- [Multi angle] $L^2$ spectral gap and group actions on Banach spaces / Author of the conference de la Salle, Mikael.
- [Multi angle] Finite quotients in coarse geometry / Author of the conference Khukhro, Anastasia.
- [Multi angle] Ideals in $L(L_p)$ / Author of the conference Johnson, William B..
Bibliography
- Ostrovskii, M.I., & Randrianantoanina, B. (2017). A new approach to low-distortion embeddings of finite metric spaces into non-superreflexive Banach spaces.
