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Israel Journal of Mathematics

, Volume 54, Issue 2, pp 129–138 | Cite as

Extensions of lipschitz maps into Banach spaces

  • William B. Johnson
  • Joram Lindenstrauss
  • Gideon Schechtman
Article

Abstract

It is proved that ifYX are metric spaces withY havingn≧2 points then any mapf fromY into a Banach spaceZ can be extended to a map\(\hat f\) fromX intoZ so that\(\left\| {\hat f} \right\|_{lip} \leqq c log n\left\| f \right\|_{lip} \) wherec is an absolute constant. A related result is obtained for the case whereX is assumed to be a finite-dimensional normed space andY is an arbitrary subset ofX.

Keywords

Hilbert Space Banach Space Absolute Constant Arbitrary Subset Open Unit Ball 
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

© Hebrew University 1986

Authors and Affiliations

  • William B. Johnson
    • 1
    • 2
  • Joram Lindenstrauss
    • 3
    • 1
  • Gideon Schechtman
    • 4
    • 1
  1. 1.Ohio State UniversityColumbusUSA
  2. 2.Texas A&M UniversityCollege StationUSA
  3. 3.The Hebrew University of JerusalemJerusalemIsrael
  4. 4.The Weizmann Institute of ScienceRehovotIsrael

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