Israel Journal of Mathematics

, Volume 132, Issue 1, pp 239–251 | Cite as

The range of the gradient of a LipschitzC 1-smooth bump in infinite dimensions

  • J. M. BorweinEmail author
  • M. Fabian
  • P. D. Loewen


If a Banach space has a LipschitzC 1-smooth bump function, then it admits other bumps of the same smoothness whose gradients exactly fill the dual unit ball and other reasonable figures. This strengthens a result of Azagra and Deville who were able to cover the dual unit ball.


Banach Space Density Character Infinite Dimension Admissible Sequence Bump 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

© Hebrew University 2002

Authors and Affiliations

  1. 1.CECMSimon Fraser UniversityBurnabyCanada
  2. 2.Mathematical InstituteCzech Academy of SciencesPraha 1Czech Republic
  3. 3.Department of MathematicsUniversity of British ColumbiaVancouverCanada

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