Real analytic approximations which almost preserve Lipschitz constants of functions defined on the Hilbert space

الأصل · EN

Let X be a separable real Hilbert space. We show that for every Lipschitz function f:X, and for every ε>0, there exists a Lipschitz, real analytic function g:X such that |f(x)-g(x)|≤ ε and Lip(g)≤ Lip(f)+ε.