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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Uniform homeomorphisms of Banach spaces and asymptotic structure


Author: N. J. Kalton
Journal: Trans. Amer. Math. Soc. 365 (2013), 1051-1079
MSC (2010): Primary 46B80, 46B20
Published electronically: September 13, 2012
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Abstract: We give a general result on the behavior of spreading models in Banach spaces which coarse Lipschitz-embed into asymptotically uniformly convex spaces. We use this result to study the uniqueness of the uniform structure in $ \ell _p$-sums of finite-dimensional spaces for $ 1<p<\infty $; in particular we give some new examples of spaces with unique uniform structure.


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Additional Information

N. J. Kalton
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05665-0
PII: S 0002-9947(2012)05665-0
Keywords: Banach spaces, uniform asymptotic convexity or smoothness, coarse embeddings, uniform homeomorphisms
Received by editor(s): February 7, 2011
Received by editor(s) in revised form: July 5, 2011
Published electronically: September 13, 2012
Additional Notes: The author acknowledges the support of NSF grant DMS-0555670.
Article copyright: © Copyright 2012 American Mathematical Society