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Keywords:

  • Constructive mathematics;
  • Banach space;
  • quasinorms;
  • pliancy;
  • uniform convexity;
  • reflexivity;
  • 46S30;
  • 03F65

We propose a natural definition of what it means in a constructive context for a Banach space to be reflexive, and then prove a constructive counterpart of the Milman-Pettis theorem that uniformly convex Banach spaces are reflexive.