Geodesic
Metric characterizations of super weakly compact operators
Studia Mathematica, Tome 239 (2017) no. 2, pp. 175-188

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We define the notion of factorization of a family of metric spaces through a bounded, linear operator between Banach spaces. This notion serves as the analogue of uniform bi-Lipschitz embeddings of this family of metric spaces into a given Banach space. We prove operator versions of well-known non-linear characterizations of superreflexivity due to Bourgain, Johnson–Schechtman, and Baudier. More precisely, we give a non-linear characterization of non-super weakly compact operators as those through which the binary tree, diamond, and Laakso graphs may be factored with uniform distortion.
DOI : 10.4064/sm8645-3-2017
Keywords: define notion factorization family metric spaces through bounded linear operator between banach spaces notion serves analogue uniform bi lipschitz embeddings family metric spaces given banach space prove operator versions well known non linear characterizations superreflexivity due bourgain johnson schechtman baudier precisely non linear characterization non super weakly compact operators those through which binary tree diamond laakso graphs may factored uniform distortion

R. M. Causey 1 ; S. J. Dilworth 1

1 
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R. M. Causey; S. J. Dilworth. Metric characterizations of super weakly compact operators. Studia Mathematica, Tome 239 (2017) no. 2, pp. 175-188. doi: 10.4064/sm8645-3-2017

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