A note on approximation of continuous functions on normed spaces

  • M.A. Mytrofanov Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, 3b Naukova str., 79060, Lviv, Ukraine
  • A.V. Ravsky Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, 3b Naukova str., 79060, Lviv, Ukraine https://orcid.org/0000-0003-2542-6959
Keywords: normed space, continuous function, analytic function, $*$-analytic function, uniform approximation, separating polynomial
Published online: 2020-06-12

Abstract


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.

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How to Cite
(1)
Mytrofanov M., Ravsky A. A Note on Approximation of Continuous Functions on Normed Spaces. Carpathian Math. Publ. 2020, 12 (1), 107-110.