http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Nonlinear classification of Banach spaces
We study the geometric classification of Banach spaces via Lipschitz, uniformly continuous, and coarse mappings. We prove that a Banach space which is uniformly homeomorphic to a linear quotient of l[subscript]p is itself a linear quotient of l[subscript]p when p<2. We show that a Banach space which is Lipschitz universal for all separable metric spaces cannot be asymptotically uniformly convex. Next we consider coarse embedding maps as defined by Gromov, and show that l[subscript]p cannot coarsely embed into a Hilbert space when p> 2. We then build upon the method of this proof to show that a quasi-Banach space coarsely embeds into a Hilbert space if and only if it is isomorphic to a subspace of L₀([mu]) for some probability space ([Omega, Beta, mu]).
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