This is an announcement for the paper "$C^k$-smooth approximations of LUR norms" by Petr Hajek and 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 $k=\infty$.

Archive classification: math.FA

Mathematics Subject Classification: 46B20, 46B03, 46E15

The source file(s), LUR3-13-1-2.tex: 67805 bytes

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http://front.math.ucdavis.edu/0901.3623

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http://arXiv.org/abs/0901.3623

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