This is an announcement for the paper "Real analytic approximations which almost preserve Lipschitz constants of functions defined on the Hilbert space" by D. Azagra, R. Fry, and L. Keener.

Abstract: Let $X$ be a separable real Hilbert space. We show that for every Lipschitz function $f:X\rightarrow\mathbb{R}$, and for every $\varepsilon>0$, there exists a Lipschitz, real analytic function $g:X\rightarrow\mathbb{R}$ such that $|f(x)-g(x)|\leq \varepsilon$ and $\textrm{Lip}(g)\leq \textrm{Lip}(f)+\varepsilon$.

Archive classification: math.FA

Mathematics Subject Classification: 46B20

Remarks: 7 pages

Submitted from: dazagra@gmail.com

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

http://front.math.ucdavis.edu/1012.4339

or

http://arXiv.org/abs/1012.4339