Fréchet differentiability of Lipschitz maps between Banach spaces

  title={Fr{\'e}chet differentiability of Lipschitz maps between Banach spaces},
  author={Joram Lindenstrauss and David Preiss},
A well-known open question is whether every countable collection of Lipschitz functions on a Banach space X with separable dual has a common point of Fréchet differentiability. We show that the answer is positive for some infinite-dimensional X. Previously, even for collections consisting of two functions this has been known for finite-dimensional X only (although for one function the answer is known to be affirmative in full generality). Our aims are achieved by introducing a new class of null… CONTINUE READING
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