• Corpus ID: 244478727

Compact retractions and Schauder decompositions in Banach spaces

  title={Compact retractions and Schauder decompositions in Banach spaces},
  author={Petr H'ajek and Rub'en Medina},
In our note we show the very close connection between the existence of a Finite Dimensional Decomposition (FDD for short) for a separable Banach space X and the existence of a Lipschitz retraction of X onto a small (in a certain precise sense) generating convex and compact subset K of X. In one direction, if X admits an FDD then we construct a Lipschitz retraction onto a small generating convex and compact set K. On the other hand, we prove that if X admits a small generating compact Lipschitz… 
3 Citations
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