$C^k$-smooth approximations of LUR norms

Petr Hajek; Antonin Prochazka

$C^k$-smooth approximations of LUR norms

Functional Analysis 2009-01-26 v1

Authors: Petr Hajek , Antonin Prochazka

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

Keywords

LUR norm C^k-smooth approximation Fr\'echet smooth norm WCG Banach space equivalent norm uniform limit

Cite

@article{arxiv.0901.3623,
  title  = {$C^k$-smooth approximations of LUR norms},
  author = {Petr Hajek and Antonin Prochazka},
  journal= {arXiv preprint arXiv:0901.3623},
  year   = {2009}
}

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