A note on approximation of continuous functions on normed spaces

M. A. Mytrofanov; A. V. Ravsky

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arXiv · 2004.00681

A note on approximation of continuous functions on normed spaces

M. A. Mytrofanov·A. V. Ravsky

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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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BibTeX RIS

M. A. Mytrofanov, A. V. Ravsky. 2020-04-01. A note on approximation of continuous functions on normed spaces. https://arxiv.org/abs/2004.00681

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