%0 Journal Article
%T $C^k$-smooth approximations of LUR norms
%A Petr Hajek
%A Antonin Prochazka
%J Mathematics
%D 2009
%I arXiv
%X 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 $k=\infty$.
%U http://arxiv.org/abs/0901.3623v1