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Geometric & Functional Analysis GAFA

, Volume 9, Issue 6, pp 1092–1127 | Cite as

Affine Approximation of Lipschitz Functions and Nonlinear Quotients

  • S. Bates
  • W. B. Johnson
  • J. Lindenstrauss
  • D. Preiss
  • G. Schechtman

Abstract.

New concepts related to approximating a Lipschitz function between Banach spaces by affine functions are introduced. Results which clarify when such approximations are possible are proved and in some cases a complete characterization of the spaces X, Y for which any Lipschitz function from X to Y can be so approximated is obtained. This is applied to the study of Lipschitz and uniform quotient mappings between Banach spaces. It is proved, in particular, that any Banach space which is a uniform quotient of L p , 1 < p < \( \infty \), is already isomorphic to a linear quotient of L p .

Keywords

Banach Space Lipschitz Function Complete Characterization Quotient Mapping Affine Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag, Basel 1999

Authors and Affiliations

  • S. Bates
    • 1
  • W. B. Johnson
    • 2
  • J. Lindenstrauss
    • 3
  • D. Preiss
    • 4
  • G. Schechtman
    • 5
  1. 1.Dept. of Math., Columbia University, New York, NY 10027, USA, e-mail: smb@math.columbia.eduUS
  2. 2.Dept. of Math., Texas A&M University, College Station, TX 77843-3368, USA, e-mail: johnson@math.tamu.eduUS
  3. 3.Inst. of Math., Hebrew University, Jerusalem, Israel, e-mail: joram@math.huji.ac.ilIL
  4. 4.Dept. of Math., University College, London, U.K., e-mail: dp@math.ucl.ac.ukGB
  5. 5.Dept. of Math., Weizmann Institute, Rehovot, Israel, e-mail: gideon@wisdom.weizmann.ac.ilIL

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