A simple proof of the approximation by real analytic Lipschitz functions

Abstract

A theorem in Azagra et al. (preprint) asserts that on a real separable Banach space with separating polynomial every Lipschitz function can be uniformly approximated by real analytic Lipschitz function with a control over the Lipschitz constant. We give a simple proof of this theorem.

Keywords

• Approximation
• Real analytic
• Lipschitz