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arXiv · 0901.3623

$C^k$-smooth approximations of LUR norms

Petr Hajek·Antonin Prochazka
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Abstract

Let $X$ be a WCG Banach space admitting a $C^k$-Fr\' echet smooth norm. Then $X$ admits an equivalent norm which is simultaneously $C^1$-Fr\' echet smooth, LUR, and a uniform limit of $C^k$-Fr\' echet smooth norms. If $X=C([0,α])$, where $α$ is an ordinal, then the same conclusion holds true with $k=\infty$.

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Petr Hajek, Antonin Prochazka. 2009-01-23. $C^k$-smooth approximations of LUR norms. https://arxiv.org/abs/0901.3623

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