Approximation of continuous functions on complex Banach spaces (Q1048605)
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scientific article; zbMATH DE number 5656358
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Approximation of continuous functions on complex Banach spaces |
scientific article; zbMATH DE number 5656358 |
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Approximation of continuous functions on complex Banach spaces (English)
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12 January 2010
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A complex analog of \textit{J. Kurzweil}'s theorem [Studia Math. 14, 255--277 (1973; Zbl 0064.10802)] on the approximation of continuous functions on separable complex Banach spaces admitting a separating polynomial is established, and a complex analysis of new results due to \textit{M. Cepedello Boiso} and \textit{P. Hájeck} [J. Math. Anal. Appl. 256, No.~1, 80--98 (2001; Zbl 0985.46009)] is obtained. To this end, the author describes a function class that is wider than the class of analytic functions and that contains the complex conjugates of analytic functions.
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analytic approximation
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uniform continuity
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Banach space
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uniform convergence
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analytic function
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polyadditive mapping
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antilinear functional
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symmetric linear operator
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Kurzweil's theorem
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