Smooth approximations of norms in separable Banach spaces
Functional Analysis
2012-08-22 v2 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.1105.6046,
title = {Smooth approximations of norms in separable Banach spaces},
author = {Petr Hájek and Jarno Talponen},
journal= {arXiv preprint arXiv:1105.6046},
year = {2012}
}
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9 pages