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


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.


Hilbert Space Banach Space Absolute Constant Arbitrary Subset Open Unit Ball 
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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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