Smooth approximations of norms in separable Banach spaces

preprint2012arXivOpen access

Abstract

Let X be a separable real Banach space having a k-times continuously Fréchet 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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