Return to search

Nonlinear classification of Banach spaces

We study the geometric classi&#64257;cation 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 lp is itself a linear quotient of lp 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 de&#64257;ned by Gromov, and show that lp 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(??) for some probability space (&#937;,B,??).

Identiferoai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/2590
Date01 November 2005
CreatorsRandrianarivony, Nirina Lovasoa
ContributorsJohnson, William B.
PublisherTexas A&M University
Source SetsTexas A and M University
Languageen_US
Detected LanguageEnglish
TypeBook, Thesis, Electronic Dissertation, text
Format262723 bytes, electronic, application/pdf, born digital

Page generated in 0.0019 seconds