Geodesic
Approximation of Continuous Functions on Complex Banach Spaces
Matematičeskie zametki, Tome 86 (2009) no. 4, pp. 557-570.

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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, analytic function, polyadditive mapping, antilinear functional, symmetric linear operator.
Mots-clés : uniform convergence 
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M. A. Mitrofanov. Approximation of Continuous Functions on Complex Banach Spaces. Matematičeskie zametki, Tome 86 (2009) no. 4, pp. 557-570. http://geodesic.mathdoc.fr/item/MZM_2009_86_4_a8/

[1] A. S. Nemirovskii, S. M. Semenov, “O polinomialnoi approksimatsii funktsii na gilbertovom prostranstve”, Matem. sb., 92:2 (1973), 257–281 | MR | Zbl

[2] J. Kurzweil, “On approximation in real Banach spaces”, Studia Math., 14 (1955), 214–231 | MR | Zbl

[3] R. M. Aron, J. B. Prolla, “Polynomial approximation of differentiable functions on Banach spaces”, J. Reine Angew. Math., 313 (1980), 195–216 | MR | Zbl

[4] J. Lesmes, “On the approximation of continuously differentiable functions in Hilbert spaces”, Rev. Colombiana Mat., 8 (1974), 217–223 | MR | Zbl

[5] L. Nachbin, “Sur les algèbres denses de fonctions différentiables sur une variété”, C. R. Acad. Sci. Paris, 228 (1949), 1549–1551 | MR | Zbl

[6] M. Cepedello Boiso, P. Hájek, “Analytic approximations of uniformly continuous functions in real Banach spaces”, J. Math. Anal. Appl., 256:1 (2001), 80–98 | DOI | MR | Zbl

[7] S. Dineen, Complex Analysis on Infinite-Dimensional Spaces, Springer Monogr. Math., Springer-Verlag, London, 1999 | MR | Zbl

[8] J. Mujica, Complex Analysis in Banach Spaces. Holomorphic Functions and Domains of Holomorphy in Finite and Infinite Dimensions, North-Holland Math. Stud., 120, North-Holland, Amsterdam, 1986 | MR | Zbl

[9] U. Rudin, Teoriya funktsii v edinichnom share iz $\mathbb C^n$, Mir, M., 1984 | MR | Zbl

[10] A. B. Aleksandrov, “Teoriya funktsii v share”, Kompleksnyi analiz – mnogie peremennye – 2, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Fundam. napravleniya, 8, VINITI, M., 1985, 115–190 | MR | Zbl

[11] R. S. Martin, Contributions to the Theory of Functionals, Ph. D. Thesis, California Institute of Technology, Pasadena, CA, 1932

[12] N. Danford, Dzh. Shvarts, Lineinye operatory. T. 1. Obschaya teoriya, IL, M., 1962 | MR | Zbl