Azagra Rueda, DanielFry, RobbKeener, L.2023-06-202023-06-2020120022-123610.1016/j.jfa.2011.09.009https://hdl.handle.net/20.500.14352/42080Let X be a separable Banach space with a separating polynomial. We show that there exists C >= 1 (depending only on X) such that for every Lipschitz function f : X -> R, and every epsilon > 0, there exists a Lipschitz, real analytic function g : X -> R such that vertical bar f (x) - g(x)vertical bar <= epsilon e and Lip(g) <= C Lip(f). This result is new even in the case when X is a Hilbert space. Furthermore, in the Hilbertian case we also show that C can be assumed to be any number greater than I.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0022123611003387restricted access517.98Real analyticApproximationLipschitz functionBanach spaceDifferentiable FunctionsPolynomialsDerivativesC(0)MapsAnálisis funcional y teoría de operadores