This is an announcement for the paper "Smooth approximations of norms in separable Banach spaces" by Petr Hajek and Jarno Talponen.

Abstract: Let X be a separable real Banach space having a k-times continuously Fr'{e}chet differentiable (i.e. C^k-smooth) norm where k=1,...,\infty. We show that any equivalent norm on X can be approximated uniformly on bounded sets by C^k-smooth norms.

Archive classification: math.FA math.AG

Mathematics Subject Classification: Primary 46B03, 46T20, Secondary 47J07, 14P20

Remarks: 10 pages

Submitted from: talponen@cc.hut.fi

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

http://front.math.ucdavis.edu/1105.6046

or

http://arXiv.org/abs/1105.6046