%0 Journal Article
%A Azagra Rueda, Daniel
%A Fry, Robb
%A Keener , L.
%T Approximation of functions and their derivatives by analytic maps on certain Banach spaces
%D 2011
%@ 0024-6093
%U https://hdl.handle.net/20.500.14352/42009
%X Let X be a separable Banach space that admits a separating polynomial; in particular, let X be a separable Hilbert space. Let f : X -> R be bounded and Lipschitz, with uniformly continuous derivative. Then, for each epsilon > 0, there exists an analytic function g : X -> R with vertical bar g - f vertical bar < epsilon and parallel to g' - f'parallel to < epsilon.
%~