Uniform homeomorphisms of Banach spaces and asymptotic structure

Kalton, N.

doi:10.1090/S0002-9947-2012-05665-0

Uniform homeomorphisms of Banach spaces and asymptotic structure
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Trans. Amer. Math. Soc. 365 (2013), 1051-1079 Request permission

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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