no. G10
Analyse fonctionnelle
Separation ratios of maps between Banach spaces
Rosendal, Christian1
1 Department of Mathematics University of Maryland, 4176 Campus Drive - William E. Kirwan Hall, College Park, MD 20742-4015, USA
Comptes Rendus. Mathématique, Tome 361 (2023) no. G10, pp. 1663-1672

Under the weak assumption on a Banach space E that E⊕E embeds isomorphically into E, we provide a characterisation of when a Banach space X coarsely embeds into E via a single numerical invariant.

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DOI : 10.5802/crmath.522
Classification : 46B80
Keywords: Coarse embeddings, Banach spaces

Rosendal, Christian 1

1 Department of Mathematics University of Maryland, 4176 Campus Drive - William E. Kirwan Hall, College Park, MD 20742-4015, USA
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     author = {Rosendal, Christian},
     title = {Separation ratios of maps between {Banach} spaces},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1663--1672},
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Rosendal, Christian. Separation ratios of maps between Banach spaces. Comptes Rendus. Mathématique, Tome 361 (2023) no. G10, pp. 1663-1672. doi: 10.5802/crmath.522

[1] Baudier, Florent Barycentric gluing and geometry of stable metrics, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM, Volume 116 (2022) no. 1, 37, 48 pages | Zbl | MR

[2] Baudier, Florent; Lancien, Gilles; Schlumprecht, Thomas The coarse geometry of Tsirelson’s space and applications, J. Am. Math. Soc., Volume 31 (2018) no. 3, pp. 699-717 | DOI | MR | Zbl

[3] Braga, Bruno Coarse and uniform embeddings, J. Funct. Anal., Volume 272 (2017) no. 5, pp. 1852-1875 | DOI | MR | Zbl

[4] Braga, Bruno On weaker notions of nonlinear embeddings between Banach spaces, J. Funct. Anal., Volume 274 (2018) no. 11, pp. 3149-3169 | DOI | MR | Zbl

[5] Casazza, Peter G.; Shura, Thaddeus J. Tsirelson’s Space, Lecture Notes in Mathematics, 1363, Springer, 1989 | DOI

[6] Figiel, Tadeusz; Johnson, William B. A uniformly convex Banach space which contains no ℓ p , Compos. Math., Volume 29 (1974), pp. 179-190 | MR

[7] Mendel, Manor; Naor, Assaf Metric Cotype, Ann. Math., Volume 168 (2008) no. 1, pp. 247-298 | DOI | MR | Zbl

[8] Naor, Assaf Uniform nonextendability from nets, C. R. Acad. Sci. Paris, Volume 353 (2015) no. 11, pp. 991-994 | DOI | MR | Numdam | Zbl

[9] Rosendal, Christian Equivariant geometry of Banach spaces and topological groups, Forum Math. Sigma, Volume 5 (2017), e22, 62 pages | MR | Zbl

[10] Rosendal, Christian Geometries of topological groups, Bull. Am. Math. Soc., Volume 60 (2023) no. 4, pp. 539-568 | DOI | MR | Zbl

[11] Rosendal, Christian On Uniform and Coarse Rigidity of L p ([0,1]), Stud. Math., Volume 268 (2023) no. 2, pp. 235-240 | DOI | MR | Zbl

[12] Tsirel’son, Boris S. It is impossible to imbed l p or c 0 into an arbitrary Banach space, Funkts. Anal. Prilozh., Volume 8 (1974), pp. 57-60 | MR

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