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The Quarterly Journal of Mathematics Advance Access originally published online on June 2, 2007
The Quarterly Journal of Mathematics 2007 58(3):393-414; doi:10.1093/qmath/ham018
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© 2007. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

COARSE AND UNIFORM EMBEDDINGS INTO REFLEXIVE SPACES

N. J. Kalton{dagger}

Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211, USA

{dagger} E-mail: nigel{at}math.missouri.edu

Received 8 December 2006; revised 20 February 2007
  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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