This article is cited in 7 papers

Approximation of Continuous Functions on Complex Banach Spaces

M. A. Mitrofanov

Ya. S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NAS Ukraine

Abstract: We prove a complex analog of Kurzweil's theorem on the approximation of continuous functions on separable Banach spaces admitting a separating polynomial and obtain a complex analog of new results due to Boiso and Hájek.

Keywords: analytic approximation, uniform continuity, Banach space, uniform convergence, analytic function, polyadditive mapping, antilinear functional, symmetric linear operator.

UDC: 517.98

Received: 19.06.2008
Revised: 17.12.2008

DOI: 10.4213/mzm5161

 English version: Mathematical Notes, 2009, 86:4, 530–541

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