rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Nonlinear classification of Banach spaces
  name:
    name part: Randrianarivony, Nirina Lovasoa, 1975-
    role:
      role term: creator
  name:
    name part: Johnson, William B.
    role:
      role term: thesis advisor.
  type of resource: text
  genre: bibliography
  origin info:
    place:
      place term: txu
    date issued: 2005
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: remote
  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]).
  note: by Nirina Lovasoa Randrianarivony.
  note: "Major Subject: Mathematics"
  note: Title from author supplied metadata (automated record created on Nov. , 09:45:50.)
  note: Vita.
  note: Abstract.
  note: Electronic resource.
  note: Mode of access: World Wide Web.
  note: System requirements: World Wide Web access and Adobe Acrobat Reader.
  note: Ph. D. Texas A&M University 2005.
  note: Includes bibliographical references.
  note: Text (Dissertation).
  subject:
    topic: Major mathematics
  subject:
    topic: nonlinear maps
  subject:
    topic: banach spaces
  identifier: http://hdl.handle.net/1969.1/2590
  record info:
    record content source: TXA
    record creation date: 061110
    record change date: 20151104084300.0
    record identifier: in00002206900