$C^k$-smooth approximations of LUR norms

Details $C^k$-smooth approximations of LUR norms $C^k$-smooth approximations of LUR norms

2009-01-23

arxiv.org/abs/0901.3623v1

Mathematics

Functional Analysis

Scientific paper

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
$X=C([0,\alpha])$, where $\alpha$ is an ordinal, then the same conclusion holds
true with $k=\infty$.

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