Lipschitz subtype

Causey, R.

doi:10.1090/tran/8216

Lipschitz subtype
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by R. M. Causey PDF

Trans. Amer. Math. Soc. 374 (2021), 1197-1227 Request permission

Abstract:

We give necessary and sufficient conditions for a Lipschitz map, or more generally a uniformly Lipschitz family of maps, to factor the Hamming cubes. This is an extension to Lipschitz maps of a particular spatial result of Bourgain, Milman, and Wolfson.

References

D. Amir and V. D. Milman, Unconditional and symmetric sets in $n$-dimensional normed spaces, Israel J. Math. 37 (1980), no. 1-2, 3–20. MR 599298, DOI 10.1007/BF02762864
B. Beauzamy, Opérateurs de type Rademacher entre espaces de Banach, Séminaire Maurey-Schwartz 1975–1976: Espaces $L^{p}$, applications radonifiantes et géométrie des espaces de Banach, Exp. Nos. 6-7, Centre Math., École Polytech., Palaiseau, 1976, pp. 29 (French). MR 0482327
J. Bourgain, V. Milman, and H. Wolfson, On type of metric spaces, Trans. Amer. Math. Soc. 294 (1986), no. 1, 295–317. MR 819949, DOI 10.1090/S0002-9947-1986-0819949-8
R. M. Causey and S. J. Dilworth, Metric characterizations of super weakly compact operators, Studia Math. 239 (2017), no. 2, 175–188. MR 3688802, DOI 10.4064/sm8645-3-2017
Ryan M. Causey, Szymon Draga, and Tomasz Kochanek, Operator ideals and three-space properties of asymptotic ideal seminorms, Trans. Amer. Math. Soc. 371 (2019), no. 11, 8173–8215. MR 3955545, DOI 10.1090/tran/7759
Javier Alejandro Chávez-Domínguez, Lipschitz $(q,p)$-mixing operators, Proc. Amer. Math. Soc. 140 (2012), no. 9, 3101–3115. MR 2917083, DOI 10.1090/S0002-9939-2011-11140-7
P. Enflo, On infinite-dimensional topological groups, Séminaire sur la Géométrie des Espaces de Banach (1977–1978), École Polytech., Palaiseau, 1978, pp. Exp. No. 10–11, 11. MR 520212
Alex Eskin, David Fisher, and Kevin Whyte, Coarse differentiation of quasi-isometries I: Spaces not quasi-isometric to Cayley graphs, Ann. of Math. (2) 176 (2012), no. 1, 221–260. MR 2925383, DOI 10.4007/annals.2012.176.1.3
Jeffrey D. Farmer and William B. Johnson, Lipschitz $p$-summing operators, Proc. Amer. Math. Soc. 137 (2009), no. 9, 2989–2995. MR 2506457, DOI 10.1090/S0002-9939-09-09865-7
L. H. Harper, Optimal numberings and isoperimetric problems on graphs, J. Combinatorial Theory 1 (1966), 385–393. MR 200192
Aicke Hinrichs, Operators of Rademacher and Gaussian subcotype, J. London Math. Soc. (2) 63 (2001), no. 2, 453–468. MR 1810141, DOI 10.1017/S0024610700001861
William B. Johnson and Gideon Schechtman, Diamond graphs and super-reflexivity, J. Topol. Anal. 1 (2009), no. 2, 177–189. MR 2541760, DOI 10.1142/S1793525309000114
Bernard Maurey and Gilles Pisier, Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach, Studia Math. 58 (1976), no. 1, 45–90 (French). MR 443015, DOI 10.4064/sm-58-1-45-90
Assaf Naor, An introduction to the Ribe program, Jpn. J. Math. 7 (2012), no. 2, 167–233. MR 2995229, DOI 10.1007/s11537-012-1222-7
M. Ribe, On uniformly homeomorphic normed spaces, Ark. Mat. 14 (1976), no. 2, 237–244. MR 440340, DOI 10.1007/BF02385837
Jörg Wenzel, Uniformly convex operators and martingale type, Rev. Mat. Iberoamericana 18 (2002), no. 1, 211–230. MR 1924692, DOI 10.4171/RMI/316