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Smooth approximations of norms in separable Banach spaces

Published 30 May 2011 in math.FA and math.AG | (1105.6046v2)

Abstract: Let X be a separable real Banach space having a k-times continuously Fr\'{e}chet differentiable (i.e. Ck-smooth) norm where k=1,...,\infty. We show that any equivalent norm on X can be approximated uniformly on bounded sets by Ck-smooth norms.

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Authors (2)

  1. Petr Hájek 
  2. Jarno Talponen 

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