Nonlinear classification of Banach spaces /
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| Format: | Thesis eBook |
| Language: | English |
| Published: |
[College Station, Tex.] :
[Texas A&M University],
[2005]
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| Online Access: | Link to OAK Trust copy |
| Abstract: | 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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| Item Description: | "Major Subject: Mathematics" Title from author supplied metadata (automated record created on Nov. , 09:45:50.) Vita. Abstract. Electronic resource. |
| Format: | Mode of access: World Wide Web. System requirements: World Wide Web access and Adobe Acrobat Reader. |
| Bibliography: | Includes bibliographical references. |