A note on approximation of continuous functions on normed spaces
Keywords: normed space, continuous function, analytic function, $*$-analytic function, uniform approximation, separating polynomial
Published online: 2020-06-12
Let $X$ be a real separable normed space $X$ admitting a separating polynomial. We prove that each continuous function from a subset $A$ of $X$ to a real Banach space can be uniformly approximated by restrictions to $A$ of functions, which are analytic on open subsets of $X$. Also we prove that each continuous function to a complex Banach space from a complex separable normed space, admitting a separating $*$-polynomial, can be uniformly approximated by $*$-analytic functions.
How to Cite
Mytrofanov M., Ravsky A. A Note on Approximation of Continuous Functions on Normed Spaces. Carpathian Math. Publ. 2020, 12 (1), 107-110.