Approximation by Lipschitz, analytic maps on certain Banach spaces

TL;DR

This paper demonstrates that on certain Banach spaces, any uniformly continuous, bounded function can be uniformly approximated by Lipschitz, analytic maps on bounded sets, expanding approximation techniques in functional analysis.

Contribution

It introduces a method to approximate uniformly continuous functions by Lipschitz, analytic maps on specific Banach spaces with separating polynomials.

Findings

Approximation of functions by Lipschitz, analytic maps on Banach spaces.

Applicable to separable Banach spaces with separating polynomials.

Enhances understanding of function approximation in infinite-dimensional spaces.

Abstract

We show that on separable Banach spaces admitting a separating polynomial, any uniformly continuous, bounded, real-valued function can be uniformly approximated by Lipschitz, analytic maps on bounded sets.