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Metric characterizations of super weakly compact operators

Volume 239 / 2017

R. M. Causey, S. J. Dilworth Studia Mathematica 239 (2017), 175-188 MSC: Primary 46B85; Secondary 47B10. DOI: 10.4064/sm8645-3-2017 Published online: 17 July 2017

Abstract

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.

Authors

  • R. M. Causey
  • S. J. Dilworth

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