Journal Article

COARSE AND UNIFORM EMBEDDINGS INTO REFLEXIVE SPACES

N. J. Kalton

in The Quarterly Journal of Mathematics

Volume 58, issue 3, pages 393-414
Published in print September 2007 | ISSN: 0033-5606
Published online June 2007 | e-ISSN: 1464-3847 | DOI: https://dx.doi.org/10.1093/qmath/ham018
COARSE AND UNIFORM EMBEDDINGS INTO REFLEXIVE SPACES

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Abstract

Answering an old problem in nonlinear theory, we show that c0 cannot be coarsely or uniformly embedded into a reflexive Banach space, but that any stable metric space can be coarsely and uniformly embedded into a reflexive space. We also show that certain quasi-reflexive spaces (such as the James space) also cannot be coarsely embedded into a reflexive space and that the unit ball of these spaces cannot be uniformly embedded into a reflexive space. We give a necessary condition for a metric space to be coarsely or uniformly embeddable in a uniformly convex space.

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Subjects: Pure Mathematics

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