TY - JOUR
AU - Mytrofanov, M.A.
AU - Ravsky, A.V.
PY - 2020/06/12
Y2 - 2023/06/05
TI - A note on approximation of continuous functions on normed spaces
JF - Carpathian Mathematical Publications
JA - Carpathian Math. Publ.
VL - 12
IS - 1
SE - Scientific articles
DO - 10.15330/cmp.12.1.107-110
UR - https://journals.pnu.edu.ua/index.php/cmp/article/view/3890
SP - 107-110
AB - 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.
ER -