Azagra Rueda, DanielFry, RobbKeener , L.2023-06-202023-06-202011-100024-609310.1112/blms/bdr032https://hdl.handle.net/20.500.14352/42009Let 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.engjournal articlehttp://blms.oxfordjournals.org/open access517.98Differentiable functionsPolynomialsExtensionsAnálisis funcional y teoría de operadores