Smooth approximations of norms in separable Banach spaces

Details Smooth approximations of norms in separable Banach spaces Smooth approximations of norms in separable Banach spaces

2011-05-30

arxiv.org/abs/1105.6046v1

Mathematics

Functional Analysis

10 pages

Scientific paper

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

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