This is an announcement for the paper "Smooth and polyhedral approximation in Banach spaces" by Victor Bible and Richard J. Smith.

Abstract: We show that norms on certain Banach spaces $X$ can be approximated uniformly, and with arbitrary precision, on bounded subsets of $X$ by $C^{\infty}$ smooth norms and polyhedral norms. In particular, we show that this holds for any equivalent norm on $c_0(\Gamma)$, where $\Gamma$ is an arbitrary set. We also give a necessary condition for the existence of a polyhedral norm on a weakly compactly generated Banach space, which extends a well-known result of Fonf.

Archive classification: math.FA

Mathematics Subject Classification: 46B03 46B20

Remarks: 12 pages

Submitted from: victor.bible@ucdconnect.ie

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1509.00369

or

http://arXiv.org/abs/1509.00369