COARSE AND UNIFORM EMBEDDINGS INTO REFLEXIVE SPACES |
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Authors: | Kalton N J |
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Institution: | Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211, USA |
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Abstract: | Answering an old problem in nonlinear theory, we show that c0cannot be coarsely or uniformly embedded into a reflexive Banachspace, but that any stable metric space can be coarsely anduniformly embedded into a reflexive space. We also show thatcertain quasi-reflexive spaces (such as the James space) alsocannot be coarsely embedded into a reflexive space and thatthe unit ball of these spaces cannot be uniformly embedded intoa reflexive space. We give a necessary condition for a metricspace to be coarsely or uniformly embeddable in a uniformlyconvex space. |
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