A note on approximation of continuous functions on normed spaces

2020/04/01 by Mytrofanov, M. A., Ravsky, A. V.
#46G20 #46T20 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2004.00681

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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