Journal Article

SMOOTH APPROXIMATIONS OF NORMS IN SEPARABLE BANACH SPACES

Petr Hájek and Jarno Talponen

in The Quarterly Journal of Mathematics

Volume 65, issue 3, pages 957-969
Published in print September 2014 | ISSN: 0033-5606
Published online December 2013 | e-ISSN: 1464-3847 | DOI: https://dx.doi.org/10.1093/qmath/hat053

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Let X be a separable real Banach space having a k-times continuously Fréchet differentiable (i.e. Ck-smooth) norm where k∈{1, …, ∞}. We show that any equivalent norm on X can be approximated uniformly on bounded sets by Ck-smooth norms.

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Subjects: Pure Mathematics